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

0,2

Links

Table of n, a(n) for n=0..95.

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.

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<h then break fi;
if type(k, integer)=true and R<2*s-m then R:=2*s-m fi;
od;
od;
od;
a(n):=R;

Crossrefs

Cf. A272894.

Sequence in context: A262906 A243607 A242472 * A319460 A343528 A161386

Adjacent sequences: A272892 A272893 A272894 * A272896 A272897 A272898

Keyword

nonn,easy

Author

Tom Mueller, May 09 2016

Status

approved