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A087522 a(0) = 2; for n>=1, a(n) = smallest prime p such that p+1 is divisible by an n-th power > 1.

%I A087522 #18 Apr 25 2019 03:36:03
%S A087522 2,2,3,7,31,31,127,127,1279,3583,5119,6143,8191,8191,81919,131071,
%T A087522 131071,131071,524287,524287,14680063,14680063,109051903,109051903,
%U A087522 654311423,738197503,738197503,2147483647,2147483647,2147483647,2147483647
%N A087522 a(0) = 2; for n>=1, a(n) = smallest prime p such that p+1 is divisible by an n-th power > 1.
%C A087522 Trivially the n-th power under consideration is 2^n for n > 1.
%H A087522 John Mason, using Robert Israel's data for A127582, <a href="/A087522/b087522.txt">Table of n, a(n) for n = 0..3310</a>
%F A087522 a(n) << 37^n by Xylouris' improvement to Linnik's theorem. - _Charles R Greathouse IV_, Dec 10 2013
%e A087522 a(1) = 2 because 3^1|3.
%e A087522 a(2) = 3 because 2^2|4.
%e A087522 a(3) = 7 because 2^3|8.
%o A087522 (PARI) okdivs(pp1, n) = fordiv(pp1, d, if ((d>1) && ispower(d, n), return (1))); 0
%o A087522 a(n) = {if (n == 0, return (2)); p = 2; while (! okdivs(p+1, n), p = nextprime(p+1)); return (p);} \\ _Michel Marcus_, Sep 14 2013
%Y A087522 A127582 is identical except for a(1).
%K A087522 nonn
%O A087522 0,1
%A A087522 _Amarnath Murthy_, Sep 11 2003
%E A087522 More terms from _Ray Chandler_, Sep 14 2003
%E A087522 Edited by _N. J. A. Sloane_, Jul 03 2008