A095237 a(1)=1; then for n even, a(n)=(sum of previous terms times n) plus 1, for n odd, a(n)=(sum of previous terms times n) minus 1.

1, 3, 11, 61, 379, 2731, 22301, 203897, 2064455, 22938391, 277554529, 3633441109, 51170962283, 771500662115, 12399117783989, 211611610180081, 3822234708877711, 72847296804492847, 1460993008134550985

Offset: 1

Author

Amarnath Murthy, Jun 13 2004

Keywords

• nonn

Comments

Conjecture: There are infinitely many primes in this sequence.

The sequence would have been a little nicer if the even terms had a minus one and the odd a plus one, so the first term would not have to be an exception.

Except for the first two terms, it appears that a(n) are the first differences of A002467. - Carl Najafi, Sep 27 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A095236.

Programs

Maple

Digits:=100: a:=n->factorial(n+1)-floor((factorial(n+1)+1)/exp(1))-factorial(n)+floor((factorial(n)+1)/exp(1)): 1,seq(a(n),n=2..20); # Muniru A Asiru, Sep 28 2018

PARI

a=vector(100); s=1; for(i=2,100,if(Mod(i,2)==0,a[i]=s*i+1,a[i]=s*i-1);s+=a[i])

Formula

a(n) = (n+1)! - floor(((n+1)!+1)/e) - n! + floor((n!+1)/e), n > 1. - Gary Detlefs, Nov 07 2010

Extensions

Edited by Johan Claes, Jun 16 2004