A124899 Sierpinski quotient ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n).

1, 7, 521, 102943, 38742049, 23775972551, 21633936185161, 27368368148803711, 45957792327018709121, 98920982783015679456199, 265572137199362841880960201, 870019499993663001431459704607, 3416070845000481662841943594125601

Offset: 1

Author

Alexander Adamchuk, Nov 12 2006

Keywords

• nonn

Comments

2n divides Sierpinski number A014566(2n-1).

2^n divides A014566(2^n-1); A014566(2^n - 1) / 2^n = A081216(2^n - 1) = A122000(n) = {1, 7, 102943, 27368368148803711, 533411691585101123706582594658103586126397951, ...}.

p+1 divides A014566(p) for prime p; A014566(p)/(p+1) = A056852(n) = {7, 521, 102943, 23775972551, 21633936185161, ...}.

Primes in this sequence are {7, 521, 45957792327018709121}.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..194
• Eric Weisstein, World of Mathematics. Sierpinski Numbers of the First Kind.

Crossrefs

Cf. A014566 (Sierpinski numbers of the first kind: n^n + 1).

Cf. A056826, A056852, A081216, A122000.

Programs

GAP

List([1..15],n->((2*n-1)^(2*n-1)+1)/(2*n)); # Muniru A Asiru, Apr 08 2018

Maple

seq(((2*n-1)^(2*n-1)+1)/(2*n),n=1..20); # Muniru A Asiru, Apr 08 2018

Mathematica

Table[((2n-1)^(2n-1)+1)/(2n),{n,1,20}]

PARI

a(n) = ((2*n-1)^(2*n-1) + 1)/(2*n); \\ Michel Marcus, Apr 08 2018

Formula

a(n) = ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n).

(2n-1)^(a(n)-1) == 1 (mod a(n)). - Thomas Ordowski, Mar 16 2021