A019460 - OEIS

%I #63 Mar 09 2021 19:11:59

%S 2,3,3,5,10,13,39,43,172,177,885,891,5346,5353,37471,37479,299832,

%T 299841,2698569,2698579,26985790,26985801,296843811,296843823,

%U 3562125876,3562125889,46307636557,46307636571,648306911994,648306912009,9724603680135,9724603680151,155593658882416

%N Add 1, multiply by 1, add 2, multiply by 2, etc., start with 2.

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

%D New York Times, Oct 13, 1996.

%H Ivan Panchenko, <a href="/A019460/b019460.txt">Table of n, a(n) for n = 0..200</a>

%H Nick Hobson, <a href="/A019460/a019460.py.txt">Python program for this sequence</a>

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

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

%F 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

%t 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 *)

%o (PARI) A019460(n)=2*(A000522(n\2)+(n\2)!)-if(bittest(n,0),1,n\2+2)

%o /* For producing the terms in increasing order, the following 'hack' can be used _M. F. Hasler_, Jan 12 2011 */

%o lastn=0; an1=1; A000522(n)={ an1=if(n, n==lastn && return(an1); n==lastn+1||error(); an1*lastn=n)+1 }

%o (Python)

%o l=[2]

%o for n in range(1, 101):

%o     l.append(l[n - 1] + ((n + 1)//2) if n%2 else l[n - 1]*(n//2))

%o print(l) # _Indranil Ghosh_, Jul 05 2017

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

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

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E One more term from _Robert G. Wilson v_, Jul 21 2009

%E Formula provided by _Nathaniel Johnston_, Nov 11 2010

%E Formula double-checked and PARI code added by _M. F. Hasler_, Nov 12 2010

%E Edited by _M. F. Hasler_, Feb 25 2018