A035103 Number of 0's in binary representation of n-th prime.

1, 0, 1, 0, 1, 1, 3, 2, 1, 1, 0, 3, 3, 2, 1, 2, 1, 1, 4, 3, 4, 2, 3, 3, 4, 3, 2, 2, 2, 3, 0, 5, 5, 4, 4, 3, 3, 4, 3, 3, 3, 3, 1, 5, 4, 3, 3, 1, 3, 3, 3, 1, 3, 1, 7, 5, 5, 4, 5, 5, 4, 5, 4, 3, 4, 3, 4, 5, 3, 3, 5, 3, 2, 3, 2, 1, 5, 4, 5, 4, 4, 4, 2, 4, 2, 2, 5, 4, 3, 2, 3, 1, 2, 2, 2, 1, 1, 7, 6, 5, 6, 5, 5, 5, 4

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014499, A035100.

Cf. A023416, A000040.

Cf. A059305.

Programs

Haskell

a035103 = a023416 . a000040  -- Reinhard Zumkeller, Feb 19 2013

Mathematica

Table[ Count[ IntegerDigits[ Prime[ n ], 2 ], 0 ], {n, 120} ]
Table[DigitCount[p,2,0],{p,Prime[Range[120]]}] (* Harvey P. Dale, Mar 03 2023 *)

PARI

A035103(n) = #(n=binary(prime(n)))-norml2(n) \\ M. F. Hasler, Nov 21 2009

Formula

a(n) = A035100(n) - A014499(n). - M. F. Hasler, Nov 21 2009

a(n) = 0 for n in { A059305 }. - Alois P. Heinz, Jun 26 2021

Extensions

More terms from Erich Friedman