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 A085080 Smallest k such that n, k and n+k have the same prime signature (canonical form), or 0 if no such number exists. 0

%I

%S 0,3,2,0,2,15,0,0,0,55,2,63,0,21,6,0,2,45,0,637,14,33,0,351,0,39,0,

%T 147,2,165,0,0,6,21,22,0,0,39,26,20237,2,231,0,325,18,39,0

%N Smallest k such that n, k and n+k have the same prime signature (canonical form), or 0 if no such number exists.

%C a(n) = 0 if n is a perfect prime power or a prime such that n+2 is composite. The zero entries in other cases suggest a generalization of Fermat's last theorem.

%C a(n) = 2 if n and n+2 form a twin prime pair.

%e a(12) = 63 as 12 + 63 = 75, 2^2*3 + 3^2*7 = 5^2*3, all have the prime signature p^2*q.

%K more,nonn

%O 1,2

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 01 2003

%E a(20)-a(47) from _Max Alekseyev_, Aug 12 2013

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Last modified February 22 06:12 EST 2019. Contains 320389 sequences. (Running on oeis4.)