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A019460 Add 1, multiply by 1, add 2, multiply by 2, etc., start with 2. 12
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
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

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Last modified July 20 15:17 EDT 2024. Contains 374459 sequences. (Running on oeis4.)