login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014566 Sierpiński numbers of the first kind: n^n + 1. 32
2, 2, 5, 28, 257, 3126, 46657, 823544, 16777217, 387420490, 10000000001, 285311670612, 8916100448257, 302875106592254, 11112006825558017, 437893890380859376, 18446744073709551617, 827240261886336764178, 39346408075296537575425, 1978419655660313589123980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Sierpiński 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, 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, Nov 12 2006

REFERENCES

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.

LINKS

M. F. Hasler, Table of n, a(n) for n = 0..100

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

Eric Weisstein's World of Mathematics, Sierpiński Number of the First Kind

FORMULA

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

E.g.f.: exp(x) + 1/(1+LambertW(-x)). - Vaclav Kotesovec, Dec 20 2014

MATHEMATICA

a(0) = 2; for n>0 Table[n^n+1, {n, 1, 20}] (* Alexander Adamchuk, Sep 11 2006 *)

PROG

(PARI) A014566(n)=n^n+1 /* M. F. Hasler, Jan 21 2009 */

(Maxima) A014566[n]:=if n=0 then 2 else n^n+1$

makelist(A014566[n], n, 0, 30); /*Martin Ettl, Oct 29 2012*/

CROSSREFS

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

Sequence in context: A154647 A103890 A292699 * A259861 A293264 A265777

Adjacent sequences:  A014563 A014564 A014565 * A014567 A014568 A014569

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 25 11:05 EST 2018. Contains 299653 sequences. (Running on oeis4.)