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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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).

Programs

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 *)

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

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

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