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

99, 180, 205, 221, 274, 293, 326, 368, 416, 529, 539, 573, 597, 602, 607, 623, 635, 639, 677, 693, 725, 785, 811, 838, 844, 852, 855, 916, 937, 939, 942, 945, 968, 997, 1028, 1093, 1130, 1151, 1203, 1227, 1252, 1304, 1311, 1349, 1508, 1514, 1519, 1523, 1540, 1547, 1629, 1636, 1641, 1654, 1656

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes listed in A031936.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10300
• Index entries for primes, gaps between.

Crossrefs

Equals A000720 o A031936.

Row 9 of A174349.

Indices of 18's in A001223.

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).

Programs

Magma

[n: n in [1..1700] | NthPrime(n+1) - NthPrime(n) eq 18]; // Vincenzo Librandi, Mar 22 2019

Mathematica

Select[Range[1700], Prime[#] + 18 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 22 2019 *)
Flatten[Position[Differences[Prime[Range[2000]]],18]] (* Harvey P. Dale, May 12 2022 *)

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

Formula

a(n) = A000720(A031936(n)).

A320707 = { i > 0 | prime(i+1) = prime(i) + 18 } = A001223^(-1)({18}).