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

1,1

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

Formula

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

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

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 *)

Prog

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

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).

Sequence in context: A124717 A126378 A342800 * A006352 A143337 A183006

Adjacent sequences: A320699 A320700 A320701 * A320703 A320704 A320705

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved