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.

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

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

Author

J. Lowell, Mar 11 2013

Extensions

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

Status

approved