A316750 -id:A316750 - cp's OEIS frontend

A316758 A self-"read and extend" sequence built following the rules visible in the Comments section.

1, 2, 4, 8, 16, 32, 46, 92, 841, 1268, 2356, 1247, 9442, 14888, 97762, 955421, 554219, 113488, 226679, 334558, 966611, 1222339, 2444678, 3456889, 9877631, 12255679, 11234558, 11224669, 22334489, 98876644, 88766449, 988775321, 9776554210, 112345589, 112246789, 122467891, 224678911, 223445789

Offset: 1

Jean-Marc Falcoz and Eric Angelini, Jul 12 2018

Start with a(1) = 1 and a(2) = 2; read the sequence digit by digit starting from the left:
when the read digit is smaller than the next one, double the last integer of the sequence and extend the sequence with the result rearranged (smallest digits first and leading zeros erased);
when the read digit is bigger than the next one, double the last integer of the sequence and extend the sequence with the result rearranged (biggest digits first, zeros at the end);
when both digits are equal, do a circular permutation of the last integer of the sequence and extend the sequence with the result (this will erase a few zeros in some cases, as 100023850 becomes 238501).

			As the only digit of a(1) = 1 is smaller than 2 (the next digit), we extend the sequence with 4 (that is 2 times 2);
as the only digit of a(2) = 2 is smaller than 4 (the next digit), we extend the sequence with 8 (that is 2 times 4);
as the only digit of a(3) = 4 is smaller than 8 (the next digit), we extend the sequence with 16 (that is 2 times 8 -- with 1 coming before 6);
as the only digit of a(4) = 8 is bigger than 1 (the next digit), we extend the sequence with 32 (that is 2 times 16 -- with 3 coming before 2);
as the first digit of a(5) = 1 is smaller than 6 (the next digit), we extend the sequence with 46 (that is 2 times 32 = 64 that is rearranged in 46);
as the last digit of a(5) = 6 is bigger than 3 (the next digit), we extend the sequence with 92 (that is 2 times 46 = 92 rearranged in 29);
. . .
as the last digit of a(9) = 1 is equal to 1 (the next digit), we extend the sequence with 554219 (this is the circular permutation of the previous term, 955421);
etc.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..3002

Cf. A316749 and A316750 (for other sets of "read and extend" rules).

A316765 A self-"read and extend" sequence built following the three rules given in the Comments section.

Original entry on oeis.org

1, 0, 2, 6, 18, 9, 27, 13, 39, 19, 9, 4, 2, 1, 0, 0, 0, 0, 0, 0, 3, 5, 7, 8, 10, 11, 5, 2, 1, 3, 1, 12, 6, 3, 1, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 15, 16, 17, 20, 21, 22, 23, 24, 12, 36, 18, 9, 4, 12, 6, 3, 9, 25, 75, 37, 111, 333, 999, 499, 1497, 4491, 2245, 6735, 3367, 10101, 5050, 15150, 7575

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Jul 12 2018

Start with a(1) = 1 and read the sequence digit by digit starting from the left:
when the read digit is odd, we divide by 2 the last term of the sequence, then extend the sequence with the entire part of the result;
when the read digit is even (but not 0), we multiply by 3 the last term of the sequence, then extend the sequence with the result;
when the read digit is 0, we extend the sequence with the smallest integer not yet present in the sequence.

			The odd digit 1 divides 1 by two (which is 0,5), and |0,5| is 0;
the digit 0 extends the sequence with the smallest integer not present yet in the sequence, which is 2;
the digit 2 multiplies 2 by three, which is 6;
the digit 6 multiplies 6 by three, which is 18;
the odd digit 1 divides 18 by two, which is 9;
the digit 8 multiplies 9 by three, which is 27; etc.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Cf. (for more self-"read and extend" sequences) A316749, A316750, A316758, A316764.

A316909 A self-"read and extend" sequence built following the three rules visible in the Comments section (a variation of A316765).

Original entry on oeis.org

1, 0, 2, 14, 4, 28, 196, 1372, 9604, 3201, 1067, 7469, 2489, 829, 276, 1932, 644, 4508, 3, 21, 7, 49, 5, 1, 0, 6, 42, 14, 4, 28, 196, 65, 455, 3185, 22295, 7431, 52017, 364119, 121373, 849611, 283203, 1982421, 660807, 220269, 73423, 513961, 3597727, 25184089, 176288623, 1234020361, 411340120, 8, 56

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Jul 16 2018

Start with a(1) = 1 and read the sequence digit by digit starting from the left:
when the read digit is odd, we divide by 3 the last term of the sequence, then extend the sequence with the entire part of the result;
when the read digit is even (but not 0), we multiply by 7 the last term of the sequence, then extend the sequence with the result;
when the read digit is 0, we extend the sequence with the smallest integer not yet present in the sequence.
This is a possible variation among many others of the first 2 rules illustrated by A316765 (where an odd digit divides by 3 and an even digit -except 0— multiplies by 2) that shows the flexibility of the "read-and-extend" idea.

			Reading the sequence one digit after the other, starting from the left:
the odd digit 1 divides 1 by three (which is 0,333...), and |0,333...| is 0;
the digit 0 extends the sequence with the smallest integer not present yet in the sequence, which is 2;
the digit 2 multiplies 2 by seven, which is 14;
the odd digit 1 divides 14 by three, (which is 4,666...) and |4,666...| is 4;
the digit 4 multiplies 4 by seven, which is 28;
the digit 4 multiplies 28 by seven, which is 196;
etc.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Cf. (for more self-"read and extend" sequences) A316749, A316750, A316758, A316764 and A316765.

cp's OEIS Frontend

A316758 A self-"read and extend" sequence built following the rules visible in the Comments section.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A316765 A self-"read and extend" sequence built following the three rules given in the Comments section.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A316909 A self-"read and extend" sequence built following the three rules visible in the Comments section (a variation of A316765).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs