A372895 - OEIS

%I #8 May 22 2024 15:12:42

%S 551,1387,2147,8119,8227,8531,10483,21907,29261,29543,30229,52909,

%T 58133,65683,73657,81257,81797,84491,89053,89281,97907,114017,184987,

%U 187891,227557,228997,238111,263017,369721,405631,436897,450607,453041,468541,472967,498817,521327,641297,732127,736003,810179,930677

%N Squarefree terms of A129802 whose prime factors are neither elite (A102742) nor anti-elite (A128852), where A129802 is the possible bases for Pepin's primality test for Fermat numbers.

%C By construction, A129802 is the disjoint union of the two following sets of numbers: (a) products of a square, some distinct anti-elite primes, an even number of elite-primes and a term here; (b) products of a square, some distinct anti-elite primes, an odd number of elite-primes and a term in A372896.

%o (PARI) isA372895(n) = {

%o if(n%2 && issquarefree(n) && isA129802(n), my(f = factor(n)~[1,]); \\ See A129802 for its program

%o for(i=1, #f, my(p=f[i], d = znorder(Mod(2, p)), StartPoint = valuation(d, 2), LengthTest = znorder(Mod(2, d >> StartPoint)), flag = 0); \\ To check if p = f[i] is an elite prime or an anti-elite prime, it suffices to check (2^2^i + 1) modulo p for StartPoint <= i <= StartPoint + LengthTest - 1; see A129802 or A372894

%o for(j = StartPoint+1, StartPoint + LengthTest - 1, if(issquare(Mod(2, p)^2^j + 1) != issquare(Mod(2, p)^2^StartPoint + 1), flag = 1; break())); if(flag == 0, return(0))); 1, 0)

%o }

%Y Cf. A129802, A102742, A128852, A372894, A372896.

%K nonn

%O 1,1

%A _Jianing Song_, May 15 2024