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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..42.

Prog

(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)
}

Crossrefs

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

Sequence in context: A127347 A351664 A063877 * A204870 A263947 A203629

Adjacent sequences: A372892 A372893 A372894 * A372896 A372897 A372898

Keyword

nonn

Author

Jianing Song, May 15 2024

Status

approved