A303845 -id:A303845 - cp's OEIS frontend

A303948 A fractal-like sequence: erasing all pairs of consecutive terms that have at least one digit in common leaves the sequence unchanged.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 30, 13, 22, 21, 33, 23, 10, 24, 14, 25, 15, 26, 16, 27, 17, 28, 18, 29, 19, 32, 31, 40, 34, 11, 20, 35, 36, 12, 30, 41, 42, 13, 22, 37, 38, 21, 33, 44, 43, 50, 45, 23, 10, 24, 39, 49, 51, 52, 14, 25, 46, 47, 15, 26, 48, 54, 16, 27, 53, 55, 17, 28

Offset: 1

Eric Angelini and Lars Blomberg, May 03 2018

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer S > 9 not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer H > 9 not yet present inside another pair of parentheses such that the integers S and H have at least one digit in common;
  4) after a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5, a(6) = 6, a(7) = 7, a(8) = 8, a(9) = 9, a(10) = 10, always try to extend the sequence with a duplicate > 9 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses;
  5) Never use a term of A171102 (Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once).

			Parentheses are added around each pair of terms having at least one digit in common:
1,2,3,4,5,6,7,8,9,(10,11),(20,12),(30,13),(22,21),(33,23),10,(24,14),(25,15),(26,16),(27,17),(28,18),(29,19),(32,31),(40,34),11,20,(35,36),12,30,(41,42),13,
Erasing all the parenthesized contents yields
1,2,3,4,5,6,7,8,9,(.....),(.....),(.....),(.....),(.....),10,(.....),(.....),(.....),(.....),(.....),(.....),(.....),(.....),11,20,(.....),12,30,(.....),13,
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A303845 for another "erasing criterion" (prime by concatenation).

A274329 Erase all pairs of contiguous terms that sum up to a prime; the remaining terms rebuild the starting sequence.

Original entry on oeis.org

1, 2, 4, 3, 1, 5, 6, 2, 4, 8, 9, 3, 1, 5, 7, 10, 6, 2, 4, 8, 12, 11, 9, 3, 1, 5, 7, 13, 16, 10, 6, 2, 4, 8, 12, 14, 15, 11, 9, 3, 1, 5, 7, 13, 17, 20, 16, 10, 6, 2, 4, 8, 12, 14, 18, 19, 15, 11, 9, 3, 1, 5, 7, 13, 17, 21, 22, 20, 16, 10, 6, 2, 4, 8, 12, 14, 18, 24, 23, 19, 15, 11, 9, 3, 1

Offset: 1

Eric Angelini, Jun 21 2016

This is the lexicographically earliest such sequence starting with a(1)=1 and showing no duplicate term in any pair to be erased.

			As a(1)=1, the next term will be a(2)=2. This pair sums up to a prime (1+2=3) and will thus be erased later.
We cannot have a(3)=3 as a(2) and a(3) also sum up to a prime (2+3=5), which is confusing [because, by construction, the same term (here "2") cannot belong to more than one pair]. Thus a(3)=4.
As the first pair (1,2) will be erased, we must erase this "4" too, else the future copy of this sequence will not start with "1,2,..."
To erase this "4" we take the smallest available integer not yet present in a pair of "erased terms" (as ruled in the "Comments" section), that will sum up to a prime with "4". This is "3" (as 4+3=7).
The next term will be "1", as this "1" doesn't sum up to a prime with "3" (the term placed before "1"), and "1" can start the future copy of this sequence.
The next term cannot be "2", because this "2" would erase "1" (2+1=3), and we don't want that. Thus a(6)=5. But if we don't erase this "5", the future copy of this sequence will start with 1,5,... which is wrong: it has to start with 1,2,... as the original one.
So "5" disappears with "6" (5+6=11), this "6" being the smallest available integer not yet present in a pair of "erased terms".
The next term can now be "2", and we see the copy of the original sequence getting slowly build (the erased terms are underlined below; the non-erased terms reproduce the original sequence):
  1,2,4,3,1,5,6,2,4,8,9,3,1,5,7,10,6,2,4,8,12,11,9,3,1,
  ^ ^ ^ ^   ^ ^     ^ ^       ^  ^          ^  ^
  5,7,13,16,10,6,2,4,8,12,14,15,11,9,3,1,5,7,13,17,20,16...
       ^  ^                ^  ^                  ^  ^

Lars Blomberg, Table of n, a(n) for n = 1..999

Cf. A303845 for another "erasing criterion" (primes by concatenation).

A302389 A fractal-like sequence: erasing all pairs of contiguous terms that don't have a digit in common leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 20, 10, 22, 21, 30, 23, 11, 1, 31, 24, 2, 12, 25, 33, 3, 13, 32, 40, 4, 14, 34, 26, 27, 35, 5, 15, 41, 28, 29, 36, 6, 16, 46, 37, 7, 17, 47, 38, 8, 18, 48, 39, 9, 19, 49, 50, 20, 10, 51, 42, 22, 21, 52

Offset: 1

Eric Angelini and Lars Blomberg, May 03 2018

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer X > 1 not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer Y > 1 not yet present inside another pair of parentheses such that X and Y have no digit in common;
  4) after a(1) = 1 and a(2) = 2, always try to extend the sequence with a duplicate > 2 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms that have no digit in common:
(1,2),(12,3),(13,4),(14,5),(15,6),(16,7),(17,8),(18,9),(19,20),(10,22),(21,30),(23,11),1,(31,24),2,12,(25,33),3,13,(32,40),4,14,
Erasing all the parenthesized contents yields
(...),(....),(....),(....),(....),(....),(....),(....),(.....),(.....),(.....),(.....),1,( .....),2,12,( .....),3,13,( .....),4,14,
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..998

For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime).

A303936 A fractal-like sequence: erasing all pairs of contiguous terms that do not sum up to a prime leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 7, 4, 13, 11, 12, 10, 19, 14, 5, 6, 17, 15, 8, 9, 20, 16, 7, 4, 13, 18, 21, 22, 23, 24, 25, 28, 26, 11, 12, 29, 27, 10, 19, 34, 30, 31, 32, 35, 33, 14, 5, 6, 17, 36, 38, 15, 8, 9, 20, 39, 37, 16, 7, 4, 13, 18, 41, 40, 21, 22, 45, 42, 47

Offset: 1

Eric Angelini, May 03 2018

nonn

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer X > 3 not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer Y > 3 not yet present inside another pair of parentheses such that X and Y sum up to a composite number;
  4) after a(1) = 1, a(2) = 2 and a(3) = 3, always try to extend the sequence with a duplicate of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms that don't sum up to a prime:
1, 2, 3, (4,5), (6,8), (9,7), 4, (13,11), (12,10), (19,14), 5, 6, (17,15), 8, 9, (20,16), 7, 4, 13,
Erasing all the parenthesized contents yields
1, 2, 3, (...), (...), (...), 4, (.....), (.....), (.....), 5, 6, (.....), 8, 9, (.....), 7, 4, 13,
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..1000

For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime), A302389 (pair having no digit in common).

A303950 A fractal-like sequence: erasing all pairs of contiguous terms that sum up to a Fibonacci number leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 4, 9, 1, 3, 5, 2, 4, 6, 7, 9, 1, 3, 8, 13, 5, 2, 4, 6, 10, 11, 7, 9, 1, 3, 8, 12, 22, 13, 5, 2, 4, 6, 10, 14, 20, 11, 7, 9, 1, 3, 8, 12, 15, 19, 22, 13, 5, 2, 4, 6, 10, 14, 16, 18, 20, 11, 7, 9, 1, 3, 8, 12, 15, 17, 38, 19, 22, 13, 5, 2, 4, 6, 10, 14, 16

Offset: 1

Eric Angelini and Lars Blomberg, May 03 2018

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer F not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer I not yet present inside another pair of parentheses such that the sum F + I is a Fibonacci number;
  4) after a(2) = 2, always try to extend the sequence with a duplicate of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms that sum up to a Fibonacci:
(1,2), (4,9), 1, (3,5), 2, 4, (6,7), 9, 1, 3, (8,13), 5, 2, 4, 6, (10,11), 7, 9, 1, 3, 8, (12,22), 13, 5, 2, 4, 6, 10, (14,20), 11, ...
Erasing all the parenthesized contents yields
(...), (...), 1, (...), 2, 4, (...), 9, 1, 3, (....), 5, 2, 4, 6, (.....), 7, 9, 1, 3, 8, (.....), 13, 5, 2, 4, 6, 10, (.....), 11, ...
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..998

Cf. A000045 (Fibonacci numbers).

For other "erasing criteria", cf. A303845 (prime by concatenation), A274329 (pair summing up to a prime), A303936 (pair not summing up to a prime), A303948 (pair sharing a digit), A302389 (pair having no digit in common).

A303951 A fractal-like sequence: erasing all pairs of contiguous terms that don't sum up to a Fibonacci number leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 3, 4, 9, 5, 3, 10, 6, 7, 8, 13, 11, 23, 12, 22, 14, 20, 15, 19, 16, 18, 17, 4, 9, 25, 21, 34, 24, 31, 26, 29, 27, 28, 30, 59, 32, 57, 33, 56, 35, 54, 36, 53, 37, 52, 38, 51, 39, 50, 40, 49, 41, 48, 42, 47, 43, 46, 44, 45, 55, 89, 58, 86, 60, 84, 61, 83

Offset: 1

Lars Blomberg and Eric Angelini, May 03 2018

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer C > 2 not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer I > 2 not yet present inside another pair of parentheses such that the sum C + I is not a Fibonacci number;
  4) after a(1) = 1 and a(2) = 2, always try to extend the sequence with a duplicate of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms that don't sum up to a Fibonacci:
1, 2, (3,4), (9,5), 3, (10,6), (7,8), (13,11), (23,12), (22,14), (20,15), (19,16), (18,17), 4, 9, (25,21), ...
Erasing all the parenthesized contents yields
1, 2, (...), (...), 3, (....), (...), (.....), (.....), (.....), (.....), (.....), (.....), 4, 9, (.....), ...
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..999

Cf. A000045 (Fibonacci numbers).

For other "erasing criteria", cf. A303845 (prime by concatenation), A274329 (pair summing up to a prime), A303936 (pair not summing up to a prime), A303948 (pair sharing a digit), A302389 (pair having no digit in common), A303950 (pair summing up to a Fibonacci).

A303953 A fractal-like sequence: erasing all pairs of contiguous terms that sum up to a square leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 10, 4, 7, 9, 5, 6, 8, 17, 10, 4, 7, 11, 14, 9, 5, 6, 8, 12, 13, 17, 10, 4, 7, 11, 15, 21, 14, 9, 5, 6, 8, 12, 16, 20, 13, 17, 10, 4, 7, 11, 15, 18, 31, 21, 14, 9, 5, 6, 8, 12, 16, 19, 30, 20, 13, 17, 10, 4, 7, 11, 15, 18, 22, 27, 31, 21, 14

Offset: 1

Lars Blomberg and Eric Angelini, May 03 2018

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer R > 3 not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer E > 3 not yet present inside another pair of parentheses such that the sum R + E is a square number;
  4) after a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4 and a(5) = 5, always try to extend the sequence with a duplicate of the oldest term > 5 of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms that sum up to a square:
1, 2, 3, (4,5), (6,10), 4, (7,9), 5, 6, (8,17), 10, 4, 7, (11,14), 9, 5, 6, 8, (12,13), 17, 10,
Erasing all the parenthesized contents yields
1, 2, 3, (...), (....), 4, (...), 5, 6, (....), 10, 4, 7, (.....), 9, 5, 6, 8, (.....), 17, 10,
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..998

Cf. A000290 (Square numbers).

For other "erasing criteria", cf. A303845 (prime by concatenation), A274329 (pair summing up to a prime), A303936 (pair not summing up to a prime), A303948 (pair sharing a digit), A302389 (pair having no digit in common), A303950 (pair summing up to a Fibonacci), A303951 (pair not summing up to a Fibonacci).

A303954 A fractal-like sequence: erasing all pairs of contiguous terms that don't sum up to a square leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 7, 3, 1, 8, 4, 5, 6, 10, 9, 16, 11, 14, 12, 13, 15, 21, 17, 19, 18, 31, 20, 29, 22, 27, 23, 2, 7, 42, 24, 25, 26, 38, 28, 36, 30, 34, 32, 49, 33, 3, 1, 8, 41, 35, 46, 37, 44, 39, 61, 40, 60, 43, 57, 45, 4, 5, 59, 47, 53, 48, 52, 50, 71, 51, 70, 54, 67

Offset: 1

Lars Blomberg and Eric Angelini, May 03 2018

The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer N not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer E not yet present inside another pair of parentheses such that the sum N + E is not a square number;
  4) after a(1) = 1 and a(2) = 2, always try to extend the sequence with a duplicate of the oldest term > 5 of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms that don't sum up to a square:
(1,2), (7,3), 1, (8,4), (5,6), (10,9), (16,11), (14,12), (13,15), (21,17), (19,18), (31,20), (29,22), (27,23), 2, 7, (42,24),
Erasing all the parenthesized contents yields
(...), (...), 1, (...), (...), (....), (.....), (.....), (.....), (.....), (.....), (.....), (.....), (.....), 2, 7, (.....),
We see that the remaining terms slowly rebuild the starting sequence.

Lars Blomberg, Table of n, a(n) for n = 1..1000

Cf. A000290 (Square numbers).

For other "erasing criteria", cf. A303845 (prime by concatenation), A274329 (pair summing up to a prime), A303936 (pair not summing up to a prime), A303948 (pair sharing a digit), A302389 (pair having no digit in common), A303950 (pair summing up to a Fibonacci), A303951 (pair not summing up to a Fibonacci), A303953 (pair summing up to a square).

A351330 A fractal-like sequence: erase all triples of contiguous terms that have an odd sum; the remaining terms rebuild the starting sequence.

Original entry on oeis.org

1, 2, 4, 6, 8, 3, 1, 2, 5, 7, 9, 4, 11, 13, 15, 6, 17, 19, 21, 8, 3, 1, 2, 5, 7, 10, 23, 12, 9, 25, 14, 16, 4, 18, 20, 27, 11, 22, 29, 24, 13, 15, 6, 17, 19, 26, 31, 28, 21, 33, 30, 32, 8, 34, 36, 35, 3, 38, 37, 40, 1, 39, 42, 44, 2, 46, 48, 41, 5, 50, 43, 52, 7, 45, 54, 56, 10, 58, 60, 47, 23, 12, 9, 25, 14

Offset: 1

Eric Angelini and Carole Dubois, Feb 07 2022

This is the lexicographically earliest such sequence starting with a(1) = 1 and showing no duplicate term in any triple to be erased.
The sequence is fractal-like as it embeds an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping triple of parentheses; a triple is made of integers X, Y and Z;
  2) always start the content inside a pair of parentheses with the smallest integer X > 1 not yet present inside another pair of parentheses and not leading to a contradiction;
  3) always follow X with the smallest integer Y > 1 not yet present inside another pair of parentheses and not leading to a contradiction;
  4) always end the content inside a pair of parentheses with the smallest integer Z > 1 not yet present inside another pair of parentheses and not leading to a contradiction such that X + Y + Z is odd;
  5) after a(1) = 1, a(2) = 2 and a(3) = 4, always try to extend the sequence with a duplicate > 2 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each triple of terms that have an odd sum:
(1, 2, 4), (6, 8, 3), 1, 2, (5, 7, 9), 4, (11, 13, 15), 6, (17, 19, 21), 8, 3, 1, 2, 5, 7, (10, 23, 12), 9, (25, 14, 16), 4, (18, 20, 27), 11, (22, 29, 24), 13, 15, 6, 17, 19, (26, 31, 28), 21, (33, 30, 32), 8, (34, 36, 35), 3, (38, 37, 40), 1, (39, 42, 44), 2,...
Erasing all the parenthesized contents yields
(...), (...), 1, 2, (...), 4, (...), 6, (...), 8, 3, 1, 2, 5, 7, (...), 9, (...), 4, (...), 11, (...), 13, 15, 6, 17, 19, (...), 21, (...), 8, (...), 3, (...), 1, (...), 2,...
We see that the remaining terms slowly rebuild the starting sequence.

Eric Angelini, Fabriquons une suite fractale, January 22nd 2022, personal blog (in French).

For other erasing criteria, cf. A303845 (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime), A351329 (triples having an even sum).

A304232 A fractal-like sequence: erasing all pairs of consecutive terms a(n) and a(n+1) having the property that the last digit of a(n) is the same as the first digit of a(n+1) leaves the sequence unchanged.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 21, 13, 12, 11, 21, 22, 20, 13, 12, 11, 21, 22, 14, 40, 20, 13, 12, 11, 21, 22, 14, 15, 50, 40, 20, 13, 12, 11, 21, 22, 14, 15, 16, 60, 50, 40, 20, 13, 12, 11, 21, 22, 14, 15, 16, 17, 70, 60, 50, 40, 20, 13, 12, 11, 21, 22, 14, 15, 16, 17, 18, 80

Offset: 1

Eric Angelini, May 08 2018

The sequence is fractal-like as it contains an infinite number of copies of itself.
The sequence was built according to these rules (see, in the Example section, the parenthesization technique):
  1) no overlapping pairs of parentheses;
  2) always start the content inside a pair of parentheses with the smallest integer S > 10 not yet present inside another pair of parentheses;
  3) always end the content inside a pair of parentheses with the smallest integer T > 10 not yet present inside another pair of parentheses such that the integer S ends with a digit d and the integer T starts with the same digit d;
  4) after a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5, a(6) = 6, a(7) = 7, a(8) = 8, a(9) = 9, a(10) = 10, always try to extend the sequence with a duplicate > 10 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

			Parentheses are added around each pair of terms such that the last digit of a(n) is the same as the first digit of a(n+1):
1,2,3,4,5,6,7,8,9,10,(11,12),11,(21,13),12,11,21,(22,20),13,12,11,21,22,(14,40),20,13,12,11,21,22,14,(15,50),40,20,
Erasing all the parenthesized contents yields
1,2,3,4,5,6,7,8,9,10,(.....),11,(.....),12,11,21,(.....),13,12,11,21,22,(.....),20,13,12,11,21,22,14,(.....),40,20,
We see that the remaining terms slowly rebuild the starting sequence.

Eric Angelini, Table of n, a(n) for n = 1..585

Cf. A303845 or A303948 (where the erasure techniques are different).

cp's OEIS Frontend

A303948 A fractal-like sequence: erasing all pairs of consecutive terms that have at least one digit in common leaves the sequence unchanged.

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A274329 Erase all pairs of contiguous terms that sum up to a prime; the remaining terms rebuild the starting sequence.

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A302389 A fractal-like sequence: erasing all pairs of contiguous terms that don't have a digit in common leaves the sequence unchanged.

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A303936 A fractal-like sequence: erasing all pairs of contiguous terms that do not sum up to a prime leaves the sequence unchanged.

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A303950 A fractal-like sequence: erasing all pairs of contiguous terms that sum up to a Fibonacci number leaves the sequence unchanged.

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A303951 A fractal-like sequence: erasing all pairs of contiguous terms that don't sum up to a Fibonacci number leaves the sequence unchanged.

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A303953 A fractal-like sequence: erasing all pairs of contiguous terms that sum up to a square leaves the sequence unchanged.

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A303954 A fractal-like sequence: erasing all pairs of contiguous terms that don't sum up to a square leaves the sequence unchanged.

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A351330 A fractal-like sequence: erase all triples of contiguous terms that have an odd sum; the remaining terms rebuild the starting sequence.

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A304232 A fractal-like sequence: erasing all pairs of consecutive terms a(n) and a(n+1) having the property that the last digit of a(n) is the same as the first digit of a(n+1) leaves the sequence unchanged.

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