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

%I A019460 #63 Mar 09 2021 19:11:59
%S A019460 2,3,3,5,10,13,39,43,172,177,885,891,5346,5353,37471,37479,299832,
%T A019460 299841,2698569,2698579,26985790,26985801,296843811,296843823,
%U A019460 3562125876,3562125889,46307636557,46307636571,648306911994,648306912009,9724603680135,9724603680151,155593658882416
%N A019460 Add 1, multiply by 1, add 2, multiply by 2, etc., start with 2.
%C A019460 After a(7) = 43, the next prime in the sequence is a(649) with 676 digits. - _M. F. Hasler_, Jan 12 2011
%D A019460 New York Times, Oct 13, 1996.
%H A019460 Ivan Panchenko, <a href="/A019460/b019460.txt">Table of n, a(n) for n = 0..200</a>
%H A019460 Nick Hobson, <a href="/A019460/a019460.py.txt">Python program for this sequence</a>
%F A019460 a(2n) = 2*(A000522(n) + n!) - n - 2.
%F A019460 a(2n+1) = 2*(A000522(n) + n!) - 1.
%F A019460 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 A019460 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 A019460 (PARI) A019460(n)=2*(A000522(n\2)+(n\2)!)-if(bittest(n,0),1,n\2+2)
%o A019460 /* For producing the terms in increasing order, the following 'hack' can be used _M. F. Hasler_, Jan 12 2011 */
%o A019460 lastn=0; an1=1; A000522(n)={ an1=if(n, n==lastn && return(an1); n==lastn+1||error(); an1*lastn=n)+1 }
%o A019460 (Python)
%o A019460 l=[2]
%o A019460 for n in range(1, 101):
%o A019460     l.append(l[n - 1] + ((n + 1)//2) if n%2 else l[n - 1]*(n//2))
%o A019460 print(l) # _Indranil Ghosh_, Jul 05 2017
%Y A019460 Cf. A019461 (same, but start with 0), A019463 (start with 1), A019462 (start with 3), A082448 (start with 4).
%Y A019460 Cf. A082458, A019464, A019465, A019466 (similar, but first multiply, then add; starting with 0,1,2,3).
%K A019460 nonn,easy
%O A019460 0,1
%A A019460 _N. J. A. Sloane_
%E A019460 One more term from _Robert G. Wilson v_, Jul 21 2009
%E A019460 Formula provided by _Nathaniel Johnston_, Nov 11 2010
%E A019460 Formula double-checked and PARI code added by _M. F. Hasler_, Nov 12 2010
%E A019460 Edited by _M. F. Hasler_, Feb 25 2018