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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
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
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.
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.
Sequence in context: A349323 A344554 A129596 * A329901 A284572 A157182
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Aug 04 2022
STATUS
approved