A108697 Numbers n such that a^r + b^r + c^r + ... is prime, where a*b*c* ... is the prime factorization of n and r is the product of the nonzero digits of n.

10, 11, 12, 14, 22, 40, 54, 101, 122, 136, 250, 261, 300, 328, 500, 539, 704, 720, 850, 1001, 1016, 1020, 1110, 1112, 1140, 1210, 1402, 2121, 2211, 2220, 2254, 2400, 3081, 3114, 3311, 4011, 4100, 4180, 4510, 6231, 9093, 10110, 10111, 10112, 10203, 10216

Offset: 1

Author

Jason Earls, Jun 19 2005

Keywords

• base
• less
• nonn

Comments

Of the terms shown, 9093 generates the largest prime, 3^243+7^243+433^243, which has 641 digits. - David Wasserman, May 22 2008

a(74) = 15273. Of the first 74 terms, a(72) = 14464 generates the largest prime, 7*2^384+113^384, which has 789 digits. - David Wasserman, May 22 2008

Examples

			22 is in the sequence because 22 = 2*11 and 2^(2*2) + 11^(2*2) = 14657, a prime.
		

Crossrefs

Cf. A051801, A082813.

A020449 is a subsequence.

Extensions

More terms from David Wasserman, May 22 2008