A073779 Number of 0's in base-3 representation of n-th prime.

0, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 3, 2, 1, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 0, 0, 3, 2, 2, 1, 2, 2, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 3, 2, 3, 2, 3, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 0, 0, 2, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 1, 4, 3, 2, 2, 2, 2, 2, 3, 2, 1, 1, 3, 2

Offset: 1

Author

Zak Seidov, Aug 11 2002

Keywords

• base
• easy
• nonn

Comments

a(n) = 0 if prime(n) is in A082555. - Robert Israel, Dec 28 2018

Examples

			a(10)=2 as 10th prime is 29 in base-10 representation, or 1002 in base-3 representation.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073780, A073781, A077267, A082555.

Programs

Magma

[ Multiplicity({* a: a in Intseq(p, 3) *}, 0): p in PrimesUpTo(600) ]; // Klaus Brockhaus, Oct 10 2010

Maple

f:= n -> numboccur(0,convert(ithprime(n),base,3)):
map(f, [$1..200]); # Robert Israel, Dec 28 2018

Mathematica

A073779[n_] := Length[Cases[IntegerDigits[Prime[n], 3], 0]];
DigitCount[#,3,0]&/@Prime[Range[120]]  (* Harvey P. Dale, Apr 26 2011 *)

Formula

a(n) = A077267(A000040(n)). - Michel Marcus, Oct 02 2013

Extensions

More terms from Klaus Brockhaus, Oct 10 2010