A320702 Indices of primes followed by a gap (distance to next larger prime) of 8.

24, 72, 77, 79, 87, 92, 94, 124, 126, 128, 132, 135, 156, 158, 166, 186, 192, 196, 220, 228, 241, 246, 248, 270, 281, 299, 304, 325, 330, 334, 338, 364, 370, 379, 386, 393, 400, 413, 417, 421, 432, 436, 454, 456, 482, 488, 507, 517, 519, 538, 589, 594, 620, 640, 661, 676, 689, 691, 712, 736, 750, 759

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes given in A031926.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10340
• Index entries for primes, gaps between

Crossrefs

Equals A000720 o A031926.

Row 4 of A174349.

Indices of 8's in A001223.

Cf. A029707, A029709, A320701, A320703, ..., A320720 (analog for gaps 2, 4, 6, 10, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Programs

Magma

[n: n in [1..800] | NthPrime(n+1) - NthPrime(n) eq 8]; // Vincenzo Librandi, Mar 21 2019

Maple

p:= 2: Res:= NULL: count:= 0:
for n from 1 while count < 100 do
  q:= nextprime(p);
  if q-p = 8 then count:= count+1; Res:= Res, n; fi;
  p:= q;
od:
Res; # Robert Israel, Oct 19 2018

Mathematica

Select[Range[800], Prime[#] + 8 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 21 2019 *)

PARI

A_vec(N=100,g=8,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)}

Formula

a(n) = A000720(A031926(n)) = A174349(4,n).

A320702 = { i > 0 | prime(i+1) = prime(i) + 8 } = A001223^(-1)({8}).