A217603 Consider sets of 3 consecutive primes a, b, c such that c - a = 100, then sequence gives the values of b.

58831, 286927, 360653, 404941, 590489, 623107, 651587, 673747, 710119, 740801, 779413, 794831, 795427, 1040311, 1107269, 1185241, 1206869, 1320437, 1392007, 1568771, 1581829, 1599803, 1601953, 1613201, 1721081, 1744927, 1942273, 1951321, 1994299, 2024063

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Zak Seidov, Table of n, a, b, c for n=1..1000

Zak Seidov, Table of n, a, b, c for n=1..1000

Example

a(1) = 58831 because {58789, 58831, 58889} is the first set of 3 consecutive primes a, b, c with c-a=100.
a(2) = 286927 because {286873, 286927, 286973} is the second set of 3 consecutive primes a, b, c with c-a=100.
a(1000) = 23090087 because {23090059, 23090087, 23090159} is the 1000th set of 3 consecutive primes a, b, c with c-a=100.

Mathematica

s = {}; a = 2; b = 3; c = 5; Do[If[c - a == 100, AppendTo[s, b]; Print[{a, b, c}]]; a = b; b = c; c = NextPrime[c], {10^5}]; s
Select[Partition[Prime[Range[151000]], 3, 1], #[[3]]-#[[1]]==100&][[;; , 2]] (* Harvey P. Dale, Jul 22 2024 *)

Prog

(PARI) p=2; q=3; forprime(r=5, 1e6, if(r-p==100, print1(q", ")); p=q; q=r) \\ Charles R Greathouse IV, Nov 14 2012

Crossrefs

Cf. A166251, A217561, A217566, A217577.

Sequence in context: A147700 A214118 A157131 * A205233 A235953 A343374

Adjacent sequences: A217600 A217601 A217602 * A217604 A217605 A217606

Keyword

nonn

Author

Zak Seidov, Oct 08 2012

Status

approved