

A073608


a(1) = 1, a(n) = smallest number such that a(n)  a(nk) is a prime power > 1 for all k.


0




OFFSET

1,2


COMMENTS

Differences a(i)a(j) are prime powers for all i,j. Conjecture: sequence is bounded.
Proof that sequence is complete: Assume there is some k after the term 12. Then {k1, k3, k5} must contain a multiple of 3. Also {k8,k10,k12} also contains a multiple of 3. No prime > 12 is a multiple of 3, so the multiples of 3 are both prime powers. This implies there must be two powers of 3 that have a difference at most 11, but no such pair exists > 12 (only 1,3 and 3,9 qualify.)  Jim Nastos, Aug 09 2002
There is an elementary proof that no set of seven integers of this kind exists.  Don Reble, Aug 10 2002


LINKS

Table of n, a(n) for n=1..6.


EXAMPLE

a(5) = 10 as 108, 105, 103, 101 or 2, 5, 7, 9 are prime powers.


CROSSREFS

Cf. A073607.
Sequence in context: A141436 A282897 A189377 * A155945 A096985 A206909
Adjacent sequences: A073605 A073606 A073607 * A073609 A073610 A073611


KEYWORD

nonn,fini,full


AUTHOR

Amarnath Murthy, Aug 04 2002


EXTENSIONS

Sixth term from Jim Nastos, Aug 09 2002


STATUS

approved



