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%I #26 Jun 17 2022 03:42:30
%S 7,89,199,1831,887,1669,2971,5591,9551,19333,15683,28229,19609,82073,
%T 43331,89689,134513,31397,212701,542603,461717,544279,927869,360653,
%U 396733,1388483,2238823,370261,5845193,1895359,6752623,3851459,1357201,6371401,7621259,11981443,2010733,8421251
%N a(n) is the smallest prime p such that the gap between p and the next prime is 4*n.
%C It is a plausible conjecture that a(n) always exists. - _N. J. A. Sloane_, Jul 21 2018
%e a(1) = A058620(1) = 7;
%e a(2) = 89 because (97 - 89)/4 = 8/4 = 2, a prime; etc.
%t 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)
%o (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
%Y Inspired by A058620. A bisection of A000230.
%K nonn
%O 1,1
%A _Zak Seidov_ and _Robert G. Wilson v_, Jun 19 2018
%E Name corrected by _Jinyuan Wang_, Jun 15 2022
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