A320704 Indices of primes followed by a gap (distance to next larger prime) of 12.

46, 47, 91, 97, 114, 121, 139, 168, 197, 203, 214, 232, 239, 240, 242, 267, 278, 280, 290, 312, 317, 342, 357, 363, 376, 381, 404, 423, 437, 439, 449, 452, 461, 470, 472, 489, 499, 511, 546, 550, 562, 565, 599, 600, 617, 633, 634, 647, 653, 657, 675, 680, 692, 698, 716, 728

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes given in A031930.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10150
• Index entries for primes, gaps between.

Crossrefs

Equals A000720 o A031930.

Row 6 of A174349.

Indices of 12's in A001223.

Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

Magma

[n: n in [1..1000] | NthPrime(n+1) - NthPrime(n) eq 12]; // Vincenzo Librandi, Mar 21 2019

Mathematica

Select[Range[1000], Prime[#] + 12 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 21 2019 *)

PARI

A320704_vec(N=100,g=12,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

Formula

a(n) = A000720(A031930(n)).

A320704 = { i > 0 | prime(i+1) = prime(i) + 12 }.