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A320707 Indices of primes followed by a gap (distance to next larger prime) of 18.

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