

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



1, 3, 11, 61, 379, 2731, 22301, 203897, 2064455, 22938391, 277554529, 3633441109, 51170962283, 771500662115, 12399117783989, 211611610180081, 3822234708877711, 72847296804492847, 1460993008134550985
(list;
graph;
refs;
listen;
history;
text;
internal format)



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*i1); s+=a[i])


CROSSREFS

Cf. A095236.
Sequence in context: A125556 A127516 A228204 * A185385 A024528 A273468
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



