A354576 -id:A354576 - cp's OEIS frontend

A354577 Variant of A253028 using only even numbers: a mirror symmetric array of even numbers where the n-th term is equal to the number of terms in the n-th row of the array.

2, 4, 6, 2, 4, 8, 10, 6, 2, 4, 8, 12, 14, 16, 18, 10, 12, 20, 22, 14, 6, 2, 4, 8, 16, 24, 26, 18, 10, 6, 2, 4, 8, 12, 20, 28, 30, 22, 14, 16, 24, 32, 34, 36, 38, 26, 28, 40, 42, 30, 18, 10, 12, 20, 32, 44, 46, 34, 22, 14, 6, 2, 4, 8, 16, 24, 36, 48, 50, 38, 26

Offset: 1

Felix Fröhlich, May 30 2022

See the examples in A253028 for a detailed illustration of how the array is constructed.

			1.........................2,4
2.......................6,2,4,8
3....................10,6,2,4,8,12
4........................14,16
5.....................18,10,12,20
6.................22,14,6,2,4,8,16,24
7..............26,18,10,6,2,4,8,12,20,28
8..................30,22,14,16,24,32
9........................34,36
10....................38,26,28,40
11..............42,30,18,10,12,20,32,44
12..........46,34,22,14,6,2,4,8,16,24,36,48
13.......50,38,26,18,10,6,2,4,8,12,20,28,40,52

Rémy Sigrist, PARI program

Cf. A253028, A354576.

PARI
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See Links section.
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A355091 Variant of A253028 using only prime numbers.

Original entry on oeis.org

2, 3, 5, 2, 7, 11, 3, 2, 5, 13, 17, 19, 23, 7, 3, 2, 5, 11, 29, 31, 13, 7, 3, 2, 2, 3, 5, 11, 17, 37, 41, 19, 43, 47, 53, 59, 23, 13, 29, 61, 67, 31, 17, 7, 5, 3, 2, 5, 7, 11, 19, 37, 71, 73, 41, 23, 13, 11, 7, 3, 2, 2, 3, 5, 11, 13, 17, 29, 43, 79

Offset: 1

Rémy Sigrist, Jun 19 2022

See the examples in A253028 for a detailed illustration of how the array is constructed:
- the n-th term gives the length of the n-th row.
- if you remove the eventual leading and trailing term in each row, you get the prime numbers, in natural order,
- repeating this procedure with the remaining terms always yields the prime numbers, in natural order.

			The first terms / rows are:
  n   a(n)  n-th row
  --  ----  ------------------------------------------------------------
   1     2                               2, 3
   2     3                             5, 2, 7
   3     5                         11, 3, 2, 5, 13
   4     2                              17, 19
   5     7                     23, 7, 3, 2, 5, 11, 29
   6    11              31, 13, 7, 3, 2, 2, 3, 5, 11, 17, 37
   7     3                            41, 19, 43
   8     2                              47, 53
   9     5                        59, 23, 13, 29, 61
  10    13          67, 31, 17, 7, 5, 3, 2, 5, 7, 11, 19, 37, 71
  11    17  73, 41, 23, 13, 11, 7, 3, 2, 2, 3, 5, 11, 13, 17, 29, 43, 79

Rémy Sigrist, Table of n, a(n) for n = 1..10022
Rémy Sigrist, PARI program

Cf. A253028, A354576, A354577.

PARI
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See Links section.
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cp's OEIS Frontend

A354577 Variant of A253028 using only even numbers: a mirror symmetric array of even numbers where the n-th term is equal to the number of terms in the n-th row of the array.

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