A055386 Smallest factor of (2n)^(2n) + 1.

5, 257, 13, 97, 101, 89, 29, 274177, 5, 148721, 5, 17, 53, 449, 17, 641, 13, 17, 5, 17, 5, 41, 29, 769, 41, 89, 13, 17, 5, 17, 5, 59649589127497217, 37, 41, 13, 97, 149, 17, 5, 15361, 5, 1753, 13, 17, 41, 449, 1129, 1153, 5, 17, 5, 1201, 17, 1777, 89, 4993, 41

Offset

1,1

Comments

If we use the commonly accepted convention that 0^0 = 1, then a(0) = 2. - Chai Wah Wu, Jul 22 2019

References

C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988. Page 82.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..313

Is there any value of n other than 1, 2 and 4, such that n^n+1 is a prime?

Formula

a(n) = A055385(2*n). - Michel Marcus, Jul 23 2013

Example

8^8 + 1 = 97 * 257 * 673, so a(4) = 97.

Mathematica

Table[With[{k = 2 n}, FactorInteger[k^k + 1]][[1, 1]], {n, 1, 60, 1} (* Vincenzo Librandi, Jul 23 2013 *)

Prog

(PARI) a(n) =  factor(n^n + 1)[1, 1] \\ Michel Marcus, Jul 23 2013

Crossrefs

Cf. A014566, A055385.

Sequence in context: A275930 A181397 A283039 * A216849 A201606 A139000

Adjacent sequences: A055383 A055384 A055385 * A055387 A055388 A055389

Keyword

nonn

Author

Walter Nissen, Jun 24 2000

Status

approved