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%I #9 Aug 08 2022 15:54:58
%S 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,
%T 18,19,17,282,62,91,61,87,21,22,20,99,295,66,97,68,92,23,25,26,154,
%U 180,319,137,114,80,94,32,27,28,189,259,205,331,146,121,82,124,36,29,33
%N 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.
%C Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...
%C This is a permutation of the positive integers > 1.
%e Array begins:
%e k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9
%e n=1: 2 3 5 7 10 13 17 20 26
%e n=2: 4 6 8 12 14 19 22 25 27
%e n=3: 9 11 15 16 18 21 23 32 36
%e n=4: 24 72 77 79 87 92 94 124 126
%e n=5: 34 42 53 61 68 80 82 101 106
%e n=6: 46 47 91 97 114 121 139 168 197
%e n=7: 30 62 66 137 146 150 162 223 250
%e n=8: 282 295 319 331 335 378 409 445 476
%e n=9: 99 180 205 221 274 293 326 368 416
%e 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).
%t gapa=Differences[Array[Prime,10000]];
%t Table[Position[gapa,2*(k-n+1)][[n,1]],{k,6},{n,k}]
%Y The row containing n is A028334(n).
%Y Row n = 1 is A029707.
%Y Row n = 2 is A029709.
%Y Column k = 1 is A038664.
%Y The column containing n is A274121(n).
%Y Column k = 2 is A356221.
%Y The diagonal A(n,n) is A356223.
%Y A001223 lists the prime gaps.
%Y A073491 lists numbers with gapless prime indices.
%Y A356224 counts even divisors with gapless prime indices, complement A356225.
%Y Cf. A066205, A119313, A193829, A287170, A328457, A356226, A356232.
%K nonn,tabl
%O 1,1
%A _Gus Wiseman_, Aug 04 2022
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