A320701 Indices of primes followed by a gap (distance to next larger prime) of 6.

9, 11, 15, 16, 18, 21, 23, 32, 36, 37, 39, 40, 51, 54, 55, 56, 58, 67, 71, 73, 74, 76, 84, 86, 96, 100, 102, 103, 105, 107, 108, 110, 111, 118, 119, 123, 129, 130, 133, 160, 161, 164, 165, 167, 170, 174, 179, 184, 185, 187, 188, 194, 195, 199, 200, 202, 208, 210, 216, 218, 219, 227, 231

Offset

1,1

Comments

Indices of the primes given in A031924.

Subsequence of indices of sexy primes A023201.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Index entries for primes, gaps between.

Formula

a(n) = A000720(A031924(n)).

A320701 = { i > 0 | prime(i+1) = prime(i) + 6 } = A001223^(-1)({6}).

Mathematica

Position[Differences[Prime[Range[250]]], 6]//Flatten (* Harvey P. Dale, Oct 13 2022 *)

Prog

(PARI) A(N=100, g=6, p=2, i=primepi(p)-1, L=List())={forprime(q=1+p, , i++; if(p+g==p=q, listput(L, i); N--||break)); Vec(L)} \\ returns the list of first N terms of the sequence

Crossrefs

Equals A000720 o A031924.

Row 3 of A174349.

Indices of 6's in A001223.

Cf. A029707, A029709, A320702, A320703, ..., A320720 (analog for gaps 2, 4, 8, 10, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Sequence in context: A348614 A113339 A270190 * A287340 A037009 A163096

Adjacent sequences: A320698 A320699 A320700 * A320702 A320703 A320704

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved