A134883 -id:A134883 - cp's OEIS frontend

A014566 Sierpiński numbers of the first kind: n^n + 1.

2, 2, 5, 28, 257, 3126, 46657, 823544, 16777217, 387420490, 10000000001, 285311670612, 8916100448257, 302875106592254, 11112006825558017, 437893890380859376, 18446744073709551617, 827240261886336764178, 39346408075296537575425, 1978419655660313589123980

Offset: 0

Eric W. Weisstein

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

Graham Everest, Alf van der Poorten, Igor Shparlinski and Thomas Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
Maohua Le, Primes in the sequences n^n+1 and n^n-1, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, pp. 156-157.
Paulo Ribenboim, The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 74, 1989.

M. F. Hasler, Table of n, a(n) for n = 0..100
Florentin Smarandache, Only Problems, Not Solutions!, Xiquan Publ. Hse., 1990, Problem 17.
Eric Weisstein's World of Mathematics, Sierpiński Number of the First Kind.

Cf. A000312, A048861, A121270, A003628, A122000, A081216, A056852, A121999, A124899, A134883.

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

A014566[n]:=if n=0 then 2 else n^n+1$
makelist(A014566[n],n,0,30); /* Martin Ettl, Oct 29 2012 */

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

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
Sum_{n>=1} 1/a(n) = A134883. - Amiram Eldar, Nov 15 2020

More terms from Erich Friedman

A134882 Decimal expansion of Sum_{x>=1} 1/(Pi^x)^(Pi^x).

Original entry on oeis.org

0, 2, 7, 4, 2, 5, 6, 9, 3, 2, 7, 6, 9, 9, 1, 3, 7, 8, 2, 8, 1, 1, 6, 1, 1, 9, 4, 8, 4, 3, 1, 2, 0, 8, 3, 2, 6, 8, 2, 2, 5, 5, 9, 5, 3, 8, 8, 0, 5, 7, 8, 9, 0, 7, 0, 9, 9, 8, 8, 1, 7, 4, 4, 3, 1, 0, 1, 6, 1, 3, 8, 6, 5, 0, 3, 8, 8, 4, 7, 4, 4, 5, 7, 6, 3, 0, 8, 4, 3, 8, 8, 3, 2, 9, 1, 7, 4, 4, 7, 1, 1

Offset: 0

Artur Jasinski, Nov 14 2007

			0.02742569327699137828116119484312083268225595388057...

Cf. A073009, A100085, A134877, A134878, A134879, A134880, A134881, A134883.

RealDigits[N[Sum[1/(Pi^n)^(Pi^n), {n, 1, 20}], 200]][[1]] (* first two zeros removed *)

A286193 Decimal expansion of Sum_{n>=1} 1/(n^n+n).

Original entry on oeis.org

7, 0, 4, 1, 8, 8, 3, 4, 9, 9, 2, 3, 3, 1, 4, 7, 1, 8, 1, 7, 1, 2, 6, 2, 0, 0, 0, 4, 4, 2, 2, 1, 8, 5, 7, 8, 0, 3, 0, 4, 1, 5, 8, 5, 3, 7, 7, 2, 9, 0, 9, 4, 4, 5, 0, 7, 4, 2, 2, 2, 3, 4, 0, 3, 8, 6, 1, 3, 9, 0, 6, 9, 3, 8, 2, 4, 0, 7, 7, 6, 1, 5, 5, 9, 0, 4, 5, 6, 8, 5, 6, 2, 3, 5, 3, 0, 5, 6

Offset: 0

Jonathan Frech, May 04 2017

			0.70418834992331471817126200044221857803...

Cf. A073009, A134883.

RealDigits[N[Sum[1/(n^n+n),{n,1,Infinity}],20]][[1]]

suminf(n=1, 1/(n^n+n)) \\ Michel Marcus, May 04 2017

from decimal import *;getcontext().prec=300;print(sum([Decimal(1)/Decimal(n**n+n)for n in range(1,200)]))

cp's OEIS Frontend

A014566 Sierpiński numbers of the first kind: n^n + 1.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Maxima

PARI

Formula

Extensions

A134882 Decimal expansion of Sum_{x>=1} 1/(Pi^x)^(Pi^x).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A286193 Decimal expansion of Sum_{n>=1} 1/(n^n+n).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Python