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

1,1

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.

Formula

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

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

Mathematica

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

Prog

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

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).

Sequence in context: A165867 A058905 A345492 * A282465 A098194 A181460

Adjacent sequences: A320701 A320702 A320703 * A320705 A320706 A320707

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved