

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



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, 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, 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
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..85.


EXAMPLE

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


CROSSREFS

First time a difference of n occurs in A025475 (with its initial 1 deleted).
Sequence in context: A135942 A181207 A068315 * A253237 A275151 A302617
Adjacent sequences: A069583 A069584 A069585 * A069587 A069588 A069589


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Mar 24 2002


EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jul 02 2002
Description corrected by Karl W. Heuer, Apr 08 2012


STATUS

approved



