The On-Line Encyclopedia of Integer Sequences (OEIS)

A356222 revision #3

A356222

Array read by antidiagonals upwards where A(n,k) is the position of the k-th appearance of 2n in the sequence of prime gaps A001223. If A001223 does not contain 2n at least k times, set A(n,k) = -1.

2, 4, 3, 9, 6, 5, 24, 11, 8, 7, 34, 72, 15, 12, 10, 46, 42, 77, 16, 14, 13, 30, 47, 53, 79, 18, 19, 17, 282, 62, 91, 61, 87, 21, 22, 20, 99, 295, 66, 97, 68, 92, 23, 25, 26, 154, 180, 319, 137, 114, 80, 94, 32, 27, 28, 189, 259, 205, 331, 146, 121, 82, 124, 36, 29, 33

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OFFSET

1,1

COMMENTS

Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...

This is a permutation of the positive integers > 1.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

Array begins:

k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9

n=1: 2 3 5 7 10 13 17 20 26

n=2: 4 6 8 12 14 19 22 25 27

n=3: 9 11 15 16 18 21 23 32 36

n=4: 24 72 77 79 87 92 94 124 126

n=5: 34 42 53 61 68 80 82 101 106

n=6: 46 47 91 97 114 121 139 168 197

n=7: 30 62 66 137 146 150 162 223 250

n=8: 282 295 319 331 335 378 409 445 476

n=9: 99 180 205 221 274 293 326 368 416

For example, the positions in A001223 of appearances of 2*3 begin: 9, 11, 15, 16, 18, 21, 23, ..., which is row n = 3 (A320701).

MATHEMATICA

gapa=Differences[Array[Prime, 10000]];

Table[Position[gapa, 2*(k-n+1)][[n, 1]], {k, 6}, {n, k}]

CROSSREFS

The row containing n is A028334(n).

Row n = 1 is A029707.

Row n = 2 is A029709.

Column k = 1 is A038664.

The column containing n is A274121(n).

Column k = 2 is A356221.

The diagonal A(n,n) is A356223.

A001223 lists the prime gaps.

A073491 lists numbers with gapless prime indices.

A356224 counts even divisors with gapless prime indices, complement A356225.

A356226 lists maximal gapless interval lengths of prime indices.

- length: A287170

- bisected length: A356229

- Heinz number: A356231

- firsts: A356232

Cf. `A000005, `A001222, `A060680, `A060681, `~A066205, A119313, ~`A137921, `A193829, ~`A328023, ~`A328335, `~A328336, ~`A328457, ~`A328458.

Sequence in context: A349323 A344554 A129596 * A329901 A284572 A157182

Adjacent sequences: A356219 A356220 A356221 * A356223 A356224 A356225

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Aug 04 2022

STATUS

editing