A320715 Indices of primes followed by a gap (distance to next larger prime) of 34.

217, 1059, 1229, 1409, 1457, 1986, 2169, 2310, 2406, 3221, 3505, 3692, 3995, 4324, 4923, 5130, 5518, 6050, 6152, 6168, 6434, 7257, 7362, 7604, 7694, 7915, 8293, 8555, 8584, 8651, 8859, 9017, 9341, 9598, 9796, 9869, 10028, 10092, 10116, 10150, 10211, 10234, 10317, 10657, 10744, 10762

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes listed in A134116.

Links

• Index entries for primes, gaps between.

Crossrefs

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).

Equals A000720 o A134116.

Indices of 34's in A001223.

Row 17 of A174349.

Programs

Mathematica

Position[Differences[Prime[Range[11000]]],34]//Flatten (* Harvey P. Dale, Jan 19 2021 *)

PARI

A(N=100,g=34,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(A134116(n)).

A320715 = { i>0 | prime(i+1) = prime(i) + 34 }.