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 #12 Sep 08 2022 08:46:23
%S 99,180,205,221,274,293,326,368,416,529,539,573,597,602,607,623,635,
%T 639,677,693,725,785,811,838,844,852,855,916,937,939,942,945,968,997,
%U 1028,1093,1130,1151,1203,1227,1252,1304,1311,1349,1508,1514,1519,1523,1540,1547,1629,1636,1641,1654,1656
%N Indices of primes followed by a gap (distance to next larger prime) of 18.
%C Indices of the primes listed in A031936.
%H Vincenzo Librandi, <a href="/A320707/b320707.txt">Table of n, a(n) for n = 1..10300</a>
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.
%F a(n) = A000720(A031936(n)).
%F A320707 = { i > 0 | prime(i+1) = prime(i) + 18 } = A001223^(-1)({18}).
%t Select[Range[1700], Prime[#] + 18 == Prime[# + 1] &] (* _Vincenzo Librandi_, Mar 22 2019 *)
%t Flatten[Position[Differences[Prime[Range[2000]]],18]] (* _Harvey P. Dale_, May 12 2022 *)
%o (PARI) A(N=100,g=18,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
%o (Magma) [n: n in [1..1700] | NthPrime(n+1) - NthPrime(n) eq 18]; // _Vincenzo Librandi_, Mar 22 2019
%Y Equals A000720 o A031936.
%Y Row 9 of A174349.
%Y Indices of 18's in A001223.
%Y 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).
%K nonn
%O 1,1
%A _M. F. Hasler_, Oct 19 2018