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%I #47 Sep 18 2017 19:55:19
%S 2,3,5,7,11,13,23,29,37,43,47,53,73,79,83,97,113,131,151,173,179,181,
%T 191,197,211,223,233,239,251,263,277,281,283,307,317,337,353,359,367,
%U 383,397,419,431,439,443,457,461,463,467,487,491,499
%N Primes p such that gpf(lpf(2^p - 1) - 1) = p.
%C This sequence has not been proved to be infinite.
%C The terms p such that 2^p - 1 is a Mersenne prime are 2, 3, 5, 7, and 13.
%C If p is prime, then gpf(lpf(2^p - 1) - 1) >= p.
%C Primes q such that gpf(lpf(2^q - 1) - 1) > q are A292237.
%H Charles R Greathouse IV, <a href="/A291691/b291691.txt">Table of n, a(n) for n = 1..119</a>
%e We have gpf(lpf(2^11 - 1) - 1) = gpf(23 - 1) = 11, so 11 is a term.
%t lpf[n_] := FactorInteger[n][[1, 1]]; gpf[n_] := FactorInteger[n][[-1, 1]]; Select[ Prime@ Range@ 45, gpf[lpf[2^# - 1] - 1] == # &] (* _Giovanni Resta_, Aug 30 2017 *)
%o (PARI) listp(nn) = forprime(p=2, nn, if (vecmax(factor(vecmin(factor(2^p-1)[,1])-1)[,1]) == p, print1(p, ", "));); \\ _Michel Marcus_, Aug 30 2017
%Y Cf. A000040, A000043, A006530, A016047, A020639, A236128.
%Y Contains A002515.
%K nonn
%O 1,1
%A _Thomas Ordowski_, Aug 30 2017
%E a(17)-a(26) from _Michel Marcus_, Aug 30 2017
%E a(27)-a(34) from _Giovanni Resta_, Aug 30 2017
%E a(35)-a(52) from _Charles R Greathouse IV_, Aug 30 2017
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