A268963 Primes 4k+1 at the end of the maximal gaps in A084162.

5, 13, 29, 89, 137, 229, 509, 1549, 1861, 9601, 15733, 16829, 33289, 39709, 50741, 180949, 183289, 1562053, 1638053, 2244157, 4469141, 4874977, 7856713, 10087481, 12021353, 12214273, 18227081, 148364081, 292182557, 320262769, 468214457, 727335397, 869766761

Offset

0,1

Comments

Subsequence of A002144.

A084161 lists the primes preceding the maximal gaps, and A084162 lists the corresponding gap sizes. See more comments there.

Links

Alexei Kourbatov, Table of n, a(n) for n = 0..42

Formula

a(n) = A084161(n) + A084162(n)

Example

a(3) = 89: There are no primes p = 1 mod 4 between 73 and 89, this gap is the largest up to 89, the gap size is 16.

Mathematica

Reap[Print[5]; Sow[5]; r = 0; p = 5; For[q = 7, q < 10^7, q = NextPrime[q], If[Mod[q, 4] == 3, Continue[]]; g = q - p; If[g > r, r = g; Print[q] Sow[q]]; p = q]][[2, 1]] (* Jean-François Alcover, Feb 20 2019, from PARI *)

Prog

(PARI) print1(5); r=0; p=5; forprime(q=7, 1e9, if(q%4==3, next); g=q-p; if(g>r, r=g; print1(", "q)); p=q)

Crossrefs

Cf. A002144, A002313, A084161, A084162.

Sequence in context: A124698 A337761 A147278 * A147349 A147288 A146420

Adjacent sequences: A268960 A268961 A268962 * A268964 A268965 A268966

Keyword

nonn

Author

Alexei Kourbatov, Feb 16 2016

Status

approved