A019460 Add 1, multiply by 1, add 2, multiply by 2, etc., start with 2.

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, 885, 891, 5346, 5353, 37471, 37479, 299832, 299841, 2698569, 2698579, 26985790, 26985801, 296843811, 296843823, 3562125876, 3562125889, 46307636557, 46307636571, 648306911994, 648306912009, 9724603680135, 9724603680151, 155593658882416

Offset

0,1

Comments

After a(7) = 43, the next prime in the sequence is a(649) with 676 digits. - M. F. Hasler, Jan 12 2011

References

New York Times, Oct 13, 1996.

Links

Ivan Panchenko, Table of n, a(n) for n = 0..200

Nick Hobson, Python program for this sequence

Formula

a(2n) = 2*(A000522(n) + n!) - n - 2.

a(2n+1) = 2*(A000522(n) + n!) - 1.

Recursive: a(0) = 2, a(n) = (1 + floor((n-1)/2) - ceiling((n-1)/2))*(a(n-1) + (n+2)/2) + (ceiling((n-1)/2) - floor((n-1)/2))*(n/2)*a(n-1). - Wesley Ivan Hurt, Jan 12 2013

Mathematica

a[n_] := If[ OddQ@n, a[n - 1] + (n + 1)/2, a[n - 1]*n/2]; a[0] = 2; Table[ a@n, {n, 0, 28}] (* Robert G. Wilson v, Jul 21 2009 *)

Prog

(PARI) A019460(n)=2*(A000522(n\2)+(n\2)!)-if(bittest(n, 0), 1, n\2+2)
/* For producing the terms in increasing order, the following 'hack' can be used M. F. Hasler, Jan 12 2011 */
lastn=0; an1=1; A000522(n)={ an1=if(n, n==lastn && return(an1); n==lastn+1||error(); an1*lastn=n)+1 }
(Python)
l=[2]
for n in range(1, 101):
    l.append(l[n - 1] + ((n + 1)//2) if n%2 else l[n - 1]*(n//2))
print(l) # Indranil Ghosh, Jul 05 2017

Crossrefs

Cf. A019461 (same, but start with 0), A019463 (start with 1), A019462 (start with 3), A082448 (start with 4).

Cf. A082458, A019464, A019465, A019466 (similar, but first multiply, then add; starting with 0,1,2,3).

Sequence in context: A228778 A296674 A297073 * A329057 A236165 A049855

Adjacent sequences: A019457 A019458 A019459 * A019461 A019462 A019463

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

One more term from Robert G. Wilson v, Jul 21 2009

Formula provided by Nathaniel Johnston, Nov 11 2010

Formula double-checked and PARI code added by M. F. Hasler, Nov 12 2010

Edited by M. F. Hasler, Feb 25 2018

Status

approved