Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Oct 13 2022 10:10:19
%S 9,11,15,16,18,21,23,32,36,37,39,40,51,54,55,56,58,67,71,73,74,76,84,
%T 86,96,100,102,103,105,107,108,110,111,118,119,123,129,130,133,160,
%U 161,164,165,167,170,174,179,184,185,187,188,194,195,199,200,202,208,210,216,218,219,227,231
%N Indices of primes followed by a gap (distance to next larger prime) of 6.
%C Indices of the primes given in A031924.
%C Subsequence of indices of sexy primes A023201.
%H Hugo Pfoertner, <a href="/A320701/b320701.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.
%F a(n) = A000720(A031924(n)).
%F A320701 = { i > 0 | prime(i+1) = prime(i) + 6 } = A001223^(-1)({6}).
%t Position[Differences[Prime[Range[250]]],6]//Flatten (* _Harvey P. Dale_, Oct 13 2022 *)
%o (PARI) A(N=100,g=6,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
%Y Equals A000720 o A031924.
%Y Row 3 of A174349.
%Y Indices of 6's in A001223.
%Y Cf. A029707, A029709, A320702, A320703, ..., A320720 (analog for gaps 2, 4, 8, 10, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
%K nonn
%O 1,1
%A _M. F. Hasler_, Oct 19 2018