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

1,1

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.

Formula

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

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

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 *)

Prog

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

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).

Sequence in context: A055164 A075815 A075814 * A235228 A157947 A097599

Adjacent sequences: A320704 A320705 A320706 * A320708 A320709 A320710

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved