A301925 a(n) is the smallest prime p such that the gap between p and the next prime is 4*n.

7, 89, 199, 1831, 887, 1669, 2971, 5591, 9551, 19333, 15683, 28229, 19609, 82073, 43331, 89689, 134513, 31397, 212701, 542603, 461717, 544279, 927869, 360653, 396733, 1388483, 2238823, 370261, 5845193, 1895359, 6752623, 3851459, 1357201, 6371401, 7621259, 11981443, 2010733, 8421251

Offset

1,1

Comments

It is a plausible conjecture that a(n) always exists. - N. J. A. Sloane, Jul 21 2018

Links

Table of n, a(n) for n=1..38.

Example

a(1) = A058620(1) = 7;
a(2) = 89 because (97 - 89)/4 = 8/4 = 2, a prime; etc.

Mathematica

t[_] := 0; p = 3; q = 5; While[p < 10000000, d = (q - p)/2; If[ t[d] == 0, t[d] = p]; p = q; q = NextPrime@ q]; t@# & /@ (2 Range@ 30)

Prog

(PARI) a(n) = {my(p = 2); forprime(q=3, , my(d = q-p); if (d/(2*n)==2, return (p)); p = q; ); } \\ Michel Marcus, Jun 22 2018; corrected Jun 15 2022

Crossrefs

Inspired by A058620. A bisection of A000230.

Sequence in context: A220357 A054678 A259360 * A036902 A142204 A071363

Adjacent sequences: A301922 A301923 A301924 * A301926 A301927 A301928

Keyword

nonn

Author

Zak Seidov and Robert G. Wilson v, Jun 19 2018

Extensions

Name corrected by Jinyuan Wang, Jun 15 2022

Status

approved