A372896 Squarefree terms of A372894 whose prime factors are neither elite (A102742) nor anti-elite (A128852).

1, 341, 671, 1891, 2117, 3277, 4033, 5461, 8249, 12557, 13021, 14531, 19171, 24811, 31609, 32777, 33437, 40951, 46139, 48929, 49981, 50737, 73279, 80581, 84169, 100253, 116143, 130289, 135923, 136271, 149437, 175577, 179783, 194417, 252361, 272491, 342151, 343027, 376169, 390641

Offset

1,2

Comments

By construction, A372894 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 A372895.

Links

Table of n, a(n) for n=1..40.

Prog

(PARI) isA372896(n) = {
if(n%2 && issquarefree(n) && isA372894(n), if(n==1, return(1)); my(f = factor(n)~[1, ]); \\ See A372894 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. A372894, A102742, A128852, A129802, A372895.

Sequence in context: A216170 A321868 A175736 * A179839 A172255 A087835

Adjacent sequences: A372893 A372894 A372895 * A372897 A372898 A372899

Keyword

nonn

Author

Jianing Song, May 15 2024

Status

approved