A348927 a(n) is the smallest prime followed by n prime gaps in arithmetic progression with a common difference of 2.

2, 5, 17, 347, 2903, 15373, 128981, 95285633, 2426256797, 41193770837, 706748065831, 68439250465123, 68439250465123

Offset

1,1

Comments

a(n) is the smallest prime p for which the n+1 consecutive primes starting at p can be written as p + c*k + k^2, 0 <= k <= n, for some c >= 0. - Pontus von Brömssen, Nov 07 2021

73389327921983 is the smallest prime followed by exactly 12 such gaps. - Martin Ehrenstein, Nov 20 2021

Links

Table of n, a(n) for n=1..13.

Example

a(2)=5, the 2 prime gaps after 5 are 2,4.
a(3)=17, the 3 prime gaps after 17 are 2,4,6.
a(4)=347, the 4 prime gaps after 347 are 2,4,6,8.
a(5)=2903, the 5 prime gaps after 2903 are 6,8,10,12,14.

Mathematica

Join[{p=2}, Table[While[Union@Differences[NextPrime[p, Range[0, n]], 2]!={2}, p=NextPrime@p]; p, {n, 2, 7}]] (* Giorgos Kalogeropoulos, Nov 05 2021 *)

Crossrefs

Cf. A349121 (same, but starting prime gap = 2), A001223 (prime gaps), A036263 (2nd differences), A158939 (monotonic increasing), A006560 (consecutive primes in arithmetic progression).

First column of A094749 (except first few terms).

Sequence in context: A111635 A041455 A376184 * A081465 A128000 A161469

Adjacent sequences: A348924 A348925 A348926 * A348928 A348929 A348930

Keyword

nonn,more

Author

Marc Morgenegg, Nov 04 2021

Extensions

a(8) from Giorgos Kalogeropoulos, Nov 05 2021

a(9) from Pontus von Brömssen, Nov 07 2021

a(10)-a(13) from Martin Ehrenstein, Nov 20 2021

Status

approved