A214074 Least m>0 such that 2^n-m and 3^n-m are relatively prime.

1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2

Offset

1,4

Comments

Conjecture: a(n) = 3 if and only if n = 330*k-209 for some k>=1.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

gcd(64-1,729-1) = 7 and gcd(64-2,729-2) = 1, so a(6) = 2.

Mathematica

Table[m = 1; While[GCD[2^n - m, 3^n - m] != 1, m++]; m, {n, 1, 140}]

Crossrefs

Cf. A214180.

Sequence in context: A095772 A305392 A175301 * A003640 A359944 A359308

Adjacent sequences: A214071 A214072 A214073 * A214075 A214076 A214077

Keyword

nonn,easy

Author

Clark Kimberling, Jul 27 2012

Status

approved