A372895 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.
551, 1387, 2147, 8119, 8227, 8531, 10483, 21907, 29261, 29543, 30229, 52909, 58133, 65683, 73657, 81257, 81797, 84491, 89053, 89281, 97907, 114017, 184987, 187891, 227557, 228997, 238111, 263017, 369721, 405631, 436897, 450607, 453041, 468541, 472967, 498817, 521327, 641297, 732127, 736003, 810179, 930677
Offset: 1
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Programs
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PARI
isA372895(n) = { if(n%2 && issquarefree(n) && isA129802(n), my(f = factor(n)~[1,]); \\ See A129802 for its program 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 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) }
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