A080085 Number of factors of 2 in the factorial of the n-th prime, counted with multiplicity.

1, 1, 3, 4, 8, 10, 15, 16, 19, 25, 26, 34, 38, 39, 42, 49, 54, 56, 64, 67, 70, 74, 79, 85, 94, 97, 98, 102, 104, 109, 120, 128, 134, 135, 145, 146, 152, 159, 162, 168, 174, 176, 184, 190, 193, 194, 206, 216, 222, 224, 228, 232, 236, 244, 255, 259, 265, 266, 273, 277

Offset

1,3

Comments

n-th prime minus number of 1's in binary representation of n-th prime. [Juri-Stepan Gerasimov, May 17 2010]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{k=1..L} floor( p_n /2^k ), where L = log(p_n)/log(2), where p_n is the n-th prime.

a(n) = A000040(n) - A014499(n). [Juri-Stepan Gerasimov, May 17 2010]

Mathematica

lst={}; Do[p=Prime[n]; s=0; While[p>1, p=IntegerPart[p/2]; s+=p; ]; AppendTo[lst, s], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 28 2009 *)

Prog

(PARI) vector(58, n, valuation(prime(n)!, 2)) \\ Arkadiusz Wesolowski, Feb 22 2014
(PARI) a(n) = prime(n) - hammingweight(prime(n)); \\ Joerg Arndt, Feb 22 2014

Crossrefs

Cf. A276133 (first differences).

Cf. A080084, A080086, A080087.

Sequence in context: A075751 A065153 A030497 * A182276 A063414 A265611

Adjacent sequences: A080082 A080083 A080084 * A080086 A080087 A080088

Keyword

nonn

Author

Paul D. Hanna, Jan 26 2003

Status

approved