cp's OEIS Frontend

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.

%I A356222 #9 Aug 08 2022 15:54:58
%S A356222 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 A356222 18,19,17,282,62,91,61,87,21,22,20,99,295,66,97,68,92,23,25,26,154,
%U A356222 180,319,137,114,80,94,32,27,28,189,259,205,331,146,121,82,124,36,29,33
%N 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.
%C A356222 Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...
%C A356222 This is a permutation of the positive integers > 1.
%e A356222 Array begins:
%e A356222         k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9
%e A356222   n=1:   2   3   5   7  10  13  17  20  26
%e A356222   n=2:   4   6   8  12  14  19  22  25  27
%e A356222   n=3:   9  11  15  16  18  21  23  32  36
%e A356222   n=4:  24  72  77  79  87  92  94 124 126
%e A356222   n=5:  34  42  53  61  68  80  82 101 106
%e A356222   n=6:  46  47  91  97 114 121 139 168 197
%e A356222   n=7:  30  62  66 137 146 150 162 223 250
%e A356222   n=8: 282 295 319 331 335 378 409 445 476
%e A356222   n=9:  99 180 205 221 274 293 326 368 416
%e A356222 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 A356222 gapa=Differences[Array[Prime,10000]];
%t A356222 Table[Position[gapa,2*(k-n+1)][[n,1]],{k,6},{n,k}]
%Y A356222 The row containing n is A028334(n).
%Y A356222 Row n = 1 is A029707.
%Y A356222 Row n = 2 is A029709.
%Y A356222 Column k = 1 is A038664.
%Y A356222 The column containing n is A274121(n).
%Y A356222 Column k = 2 is A356221.
%Y A356222 The diagonal A(n,n) is A356223.
%Y A356222 A001223 lists the prime gaps.
%Y A356222 A073491 lists numbers with gapless prime indices.
%Y A356222 A356224 counts even divisors with gapless prime indices, complement A356225.
%Y A356222 Cf. A066205, A119313, A193829, A287170, A328457, A356226, A356232.
%K A356222 nonn,tabl
%O A356222 1,1
%A A356222 _Gus Wiseman_, Aug 04 2022