A356221 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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, ...

LINKS

Table of n, a(n) for n=1..45.

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&]]}]

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.

Sequence in context: A180483 A348409 A348254 * A102253 A359799 A246210

Adjacent sequences: A356218 A356219 A356220 * A356222 A356223 A356224

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 02 2022

STATUS

approved