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

1,2

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

Formula

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

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

Prog

(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])

Crossrefs

Cf. A095236.

Sequence in context: A125556 A127516 A228204 * A185385 A024528 A368880

Adjacent sequences: A095234 A095235 A095236 * A095238 A095239 A095240

Keyword

nonn

Author

Amarnath Murthy, Jun 13 2004

Extensions

Edited by Johan Claes, Jun 16 2004

Status

approved