A356221 Position of second appearance of 2n in the sequence of prime gaps A001223; if 2n does not appear at least twice, a(n) = -1.

3, 6, 11, 72, 42, 47, 62, 295, 180, 259, 297, 327, 446, 462, 650, 1315, 1059, 1532, 4052, 2344, 3732, 3861, 8805, 7234, 4754, 2810, 4231, 14124, 5949, 9834, 17200, 10229, 19724, 25248, 15927, 30765, 42673, 28593, 24554, 50523, 44227, 44390, 29040, 89715, 47350

Offset: 1

Author

Gus Wiseman, Aug 02 2022

Keywords

• nonn

Comments

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

Crossrefs

The position of the first (instead of second) appearance of 2n is A038664.

Column k = 2 of A356222.

The position of the n-th appearance of 2n is A356223.

A001223 lists the prime gaps, reduced A028334.

A073491 lists numbers with gapless prime indices.

A274121 counts appearances of the n-th prime gap in those prior.

A356226 gives the lengths of maximal gapless intervals of prime indices.

Cf. A029709, A066205, A137921, A193829, A287170, A328335, A328457, A356224, A356225.

Programs

Mathematica

nn=1000;
gaps=Differences[Array[Prime,nn]];
mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
Table[Position[gaps,2*n][[2,1]],{n,mnrm[Select[Range[nn],Length[Position[gaps,2*#]]>=2&]]}]