

A216185


a(n) is the smallest odd number k with GCD(k,n)=1 such that all the powers of 2 mod k are distinct from n mod k, or 0 if n is a power of 2.


1



0, 7, 0, 7, 7, 15, 0, 31, 7, 15, 7, 7, 15, 23, 0, 7, 31, 7, 7, 23, 15, 17, 7, 31, 7, 7, 15, 15, 23, 7, 0, 7, 7, 39, 31, 15, 7, 17, 7, 7, 23, 15, 15, 7, 17, 7, 7, 31, 31, 23, 7, 23, 7, 7, 15, 17, 15, 7, 23, 7, 7, 17, 0, 17, 7, 15, 7, 7, 39, 15, 31, 7, 15, 7, 7
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OFFSET

2,2


COMMENTS

All nonzero values are >= 7.


LINKS

Table of n, a(n) for n=2..76.


EXAMPLE

a(3) = 7 because the powers of 2 mod 7 are 2,4,1,2,4,1,2,4,1,2,4,... (and 3 never appears).


PROG

(PARI) a216185(n) = {local(k, m); if((omega(n) == 1) && (Mod(n, 2) == Mod(0, 2)), return(0), k=3; while(gcd(k, n) != 1  (sum(m=0, eulerphi(k)  1, (Mod(2, k)^m == Mod(n, k))) >= 1), k = k+2)); k} \\ Michael B. Porter, Mar 16 2013


CROSSREFS

Sequence in context: A341273 A011438 A321022 * A202996 A019597 A096444
Adjacent sequences: A216182 A216183 A216184 * A216186 A216187 A216188


KEYWORD

nonn,changed


AUTHOR

J. Lowell, Mar 11 2013


EXTENSIONS

a(34)a(76) from Michael B. Porter, Mar 16 2013


STATUS

approved



