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A069586 Smallest prime power p^k (k>=2) such that there is a difference of exactly n between p^k and some other prime power q^l (l >= 2); or 0 if no such q^l exists. 1

%I

%S 8,25,125,4,4,0,9,8,16,2187,16,4,243,0,49,9,8,9,8,0,4,27,4,8,0,0,0,4,

%T 0,6859,0,32,16,0,0,0,27,1331,25,9,8,0,0,81,4,243,81,16,32,0,0,0,0,27,

%U 9,8,64,0,0,4,64,0,961,64,16,0,0,0,0,0,0,9,8,169,0,49,4,0,49,0,0,0,0,0,0

%N Smallest prime power p^k (k>=2) such that there is a difference of exactly n between p^k and some other prime power q^l (l >= 2); or 0 if no such q^l exists.

%C Any solution for the terms that are currently zero is > 10^14. Since there are so many 'missing' values, I would recommend leaving the more keyword. - Larry Reeves (larryr(AT)acm.org), Jul 02 2002

%e a(1) = 8 = 2^3 and 8+1 = 9=3^2; a(3) = 125 = 5^3 and 125 +3 =128 = 2^7.

%Y First time a difference of n occurs in A025475 (with its initial 1 deleted).

%K nonn

%O 1,1

%A _Amarnath Murthy_, Mar 24 2002

%E More terms from Larry Reeves (larryr(AT)acm.org), Jul 02 2002

%E Description corrected by Karl W. Heuer, Apr 08 2012

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)