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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
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, 147, 2, 165, 0, 0, 6, 21, 22, 0, 0, 39, 26, 20237, 2, 231, 0, 325, 18, 39, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

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

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

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

CROSSREFS

Sequence in context: A131728 A075115 A273528 * A260308 A079714 A286889

Adjacent sequences:  A085077 A085078 A085079 * A085081 A085082 A085083

KEYWORD

more,nonn

AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 01 2003

EXTENSIONS

a(20)-a(47) from Max Alekseyev, Aug 12 2013

STATUS

approved

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Last modified October 20 04:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)