A209332 a(n) is the minimal positive number k such that n<+>k is prime or 0 if no such number exists (operation <+> defined in A206853).

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 0, 3, 1, 1, 1, 1, 2, 4, 0, 3, 2, 1, 0, 4, 1, 1, 1, 1, 1, 2, 1, 1, 0, 5, 0, 3, 2, 1, 0, 7, 2, 2, 1, 1, 2, 1, 0, 8, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 7, 1, 2, 1, 1, 3, 2, 1, 1, 0, 3, 0, 4, 3

Offset: 1

Author

Vladimir Shevelev, Mar 06 2012

Keywords

• nonn
• base

Comments

Numbers n for which a(n) = 1 form sequence A208982.

a(n) = 0 for n = 25, 33, 37, 47,... (A209333).

A simple sufficient condition for a(n) = 0 (which is proved by induction) is that n<+>k is not prime up to the moment that n<+>k is even and n<+>(k+1)-n<+>k = 2^t, where t >= m+1 and m defined by the condition 2^m <= n < 2^(m+1).

Conjecture: for even n, a(n) > 0.

Crossrefs

Cf. A205509, A205510, A205511, A205302, A205649, A205533, A122565, A206852, A206853, A206960, A209085, A208982, A209085, A209333.