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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, 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
1,7
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.
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Mar 06 2012
STATUS
approved