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

1,1

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

Links

Table of n, a(n) for n=1..46.

Example

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.

Sequence in context: A098945 A323190 A046431 * A109279 A258744 A219251

Adjacent sequences: A108694 A108695 A108696 * A108698 A108699 A108700

Keyword

base,less,nonn

Author

Jason Earls, Jun 19 2005

Extensions

More terms from David Wasserman, May 22 2008

Status

approved