A073587 a(n) = a(n-1)*2^n + 1 where a(0)=1.

1, 3, 13, 105, 1681, 53793, 3442753, 440672385, 112812130561, 57759810847233, 59146046307566593, 121131102837896382465, 496152997224023582576641, 4064485353259201188467843073, 66592528027798752271857140908033, 2182103958414909514444214793274425345

Offset

0,2

Comments

Also, number of nodes in an n-ary tree with increasing fanout as the level increases. - Dhruv Matani, Apr 12 2012

We have 1 = gcd(a(n), a(n+1)) for all n>=0. The sequence gcd(a(n), a(n+2)) has period 14, while gcd(a(n), a(n+3)) has period 12. - Michael Somos, Nov 30 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 0..81

Formula

a(n) = floor(D*2^(n*(n+1)/2)) where D is a constant, D=1.64163256065515386629... = Sum_{k>=0} 1/2^(k(k+1)/2) = A299998. - Benoit Cloitre, Sep 01 2002

a(n)*(a(n+2)-1) = 2*a(n+1)*(a(n+1)-1) for all n>=0. - Michael Somos, Nov 30 2025

Mathematica

a = 1; Table[a = a*2^n + 1, {n, 14}] (* Jayanta Basu, Jul 02 2013 *)
nxt[{n_, a_}]:={n+1, a 2^(n+1)+1}; NestList[nxt, {0, 1}, 20][[;; , 2]] (* Harvey P. Dale, Jan 31 2026 *)

Prog

(UBASIC)
25 A=1
30 for I=1 to 20
40 A=A*2^I+1
50 print A
60 next
70 end

Crossrefs

Cf. A000225 (nodes in a binary tree).

Cf. A006125, A117261, A299998.

Sequence in context: A098027 A357247 A182104 * A366698 A337869 A377827

Adjacent sequences: A073584 A073585 A073586 * A073588 A073589 A073590

Keyword

easy,nonn

Author

Felice Russo, Aug 28 2002

Extensions

Added a(0)=1. Added information from duplicate sequence A182104. - N. J. A. Sloane, Dec 28 2015

Status

approved