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

Author

Alexei Kourbatov, Feb 16 2016

Keywords

• nonn

Comments

Subsequence of A002144.

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A002144, A002313, A084161, A084162.

Programs

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 *)

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)

Formula

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