A272895 a(n) is the largest natural number k such that the composite number (2n+1) 2^k+1 has a nontrivial divisor of the form h2^s+1 (h odd) with 2s>k. If such a natural number does not exist, we set a(n)=0.
0, 3, 4, 5, 5, 2, 6, 7, 6, 4, 3, 4, 7, 1, 8, 9, 8, 6, 3, 4, 6, 5, 1, 6, 8, 2, 6, 3, 9, 4, 10, 11, 10, 8, 4, 6, 5, 5, 5, 9, 6, 7, 2, 3, 8, 7, 3, 8, 9, 4, 8, 4, 4, 6, 4, 9, 10, 6, 7, 4, 11, 3, 12, 13, 12, 10, 5, 8, 8, 6, 6, 6, 5, 6, 6, 7, 3, 5, 10, 4, 8, 9, 0, 4, 8, 4, 5, 11, 8, 8, 3, 6, 10, 9, 4, 10
Offset: 0
Links
- Tom Müller, On the Exponents of Non-Trivial Divisors of Odd Numbers and a Generalization of Proth's Primality Theorem, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.7.
Crossrefs
Cf. A272894.
Programs
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Maple
H:=2n+1: smax:=floor(evalf(log[2](H))): R:=A272894(n) for m from 0 to smax do; for s from m+1 to smax+1 do; hmax:=floor(evalf(H/2^m)): for h from 1 to hmax by 2 do; k:=(2^(s-m)*H-h)/(2^s*h+1); if k