0,1

Sierpinski primes of the form n^n + 1 are {2,5,257,...} = A121270. The prime p divides a((p-1)/2) for p = {5,7,13,23,29,31,37,47,53,61,71,...} = A003628 Primes congruent to {5, 7} mod 8. p^2 divides a((p-1)/2) for prime p = {29,37,3373,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 11 2006

n divides a(n-1) for even n, or 2n divides a(2n-1). a(2n-1)/(2n) = A124899(n) = {1, 7, 521, 102943, 38742049, 23775972551, 21633936185161, 27368368148803711, 45957792327018709121, ...}. 2^n divides a(2^n-1). A014566[2^n - 1] / 2^n = A081216[2^n - 1] = A122000[n] = {1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, ...}. p+1 divides a(p) for prime p. a(p)/(p+1) = A056852[n] = {7, 521, 102943, 23775972551, 21633936185161, ...}. p^2 divides a((p-1)/2) for prime p = {29, 37, 3373} = A121999(n). - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 12 2006

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

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.

P. Ribenboim, The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 74, 1989.

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!.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

For n>0, resultant of x^n+1 and nx-1. - Ralf Stephan, Nov 20 2004

a(0) = 2; for n>0 Table[n^n+1, {n, 1, 20}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 11 2006

Cf. A000312, A048861, A121270, A003628, A122000, A081216, A056852, A121999, A124899.

Adjacent sequences: A014563 A014564 A014565 this_sequence A014567 A014568 A014569

Sequence in context: A032130 A019099 A103890 this_sequence A076658 A020549 A114715

nonn,easy

Eric Weisstein (eric(AT)weisstein.com)

More terms from Erich Friedman (erich.friedman(AT)stetson.edu).