1,2

a(n) is divisible by (n - 1). Corresponding quotients are a(n)/(n - 1) = {1, 3, 13, 85, 781, 9331, ...} = A023037(n). p divides a(p-1) for prime p. p divides a((p-1)/2) for prime p = {3,11,17,19,41,43,59,67,73,83,89,97,...} = A033200 Primes congruent to {1, 3} mod 8; or, odd primes of form x^2+2*y^2. p divides a((p-1)/3) for prime p = {61,67,73,103,151,193,271,307,367,...} = A014753 3 and -3 are both cubes (one implies other) mod these primes p=1 mod 6. p divides a((p-1)/4) for prime p = {5,13,17,29,37,41,53,61,73,...} = A002144 Pythagorean primes: primes of form 4n+1. p divides a((p-1)/5) for prime p = {31,191,251,271,601,641,761,1091,...}. p divides a((p-1)/6) for prime p = {7,241,313,337,409,439,607,631,727,751,919,937,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 22 2007

M. Le, Primes in the sequences n^n+1 and n^n-1, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 156-157.

F. Smarandache, Only Problems, Not Solutions!, Xiquan Publ. Hse., 1990, Problem 17.

M. L. Perez et al., eds., Smarandache Notions Journal

F. Smarandache, Only Problems, Not Solutions!

Cf. A000312, A048860.

Cf. A023037, A033200, A014753, A002144.

Adjacent sequences: A048858 A048859 A048860 this_sequence A048862 A048863 A048864

Sequence in context: A067858 A052141 A062793 this_sequence A053972 A126738 A119293

nonn,easy

Charles T. Le (charlestle(AT)yahoo.com)

Extended (and corrected) by Patrick De Geest (pdg(AT)worldofnumbers.com), 7/99.