A104638 Number of odd digits in n-th prime.

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

Offset

1,5

Comments

The only zero is the first term. Sequence is unbounded. - Zak Seidov, Jan 12 2016

From Robert Israel, Jan 12 2016: (Start)

For any N, the asymptotic density of terms >= N is 1.

On the other hand, a(n) = 2 if prime(n) is in A159352, which is conjectured to be infinite.

Record values: a(2) = 1, a(5) = 2, a(30) = 3, a(187) = 4, a(1346) = 5, a(10545) = 6, a(86538) = 7, a(733410) = 8.

(End)

Links

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

Formula

a(n) = A196564(A000040(n)). - Michel Marcus, Oct 05 2013

Maple

seq(nops(select(type, convert(ithprime(i), base, 10), odd)), i=1..100); # Robert Israel, Jan 12 2016

Mathematica

Table[Count[IntegerDigits[Prime[n]], _?OddQ], {n, 100}] (* Harvey P. Dale, Jan 22 2012 *)
Table[Total[Mod[IntegerDigits[Prime[n]], 2]], {n, 100}] (* Vincenzo Librandi, Jan 13 2016 *)

Prog

(PARI) a(n)=vecsum(digits(prime(n)%2)) \\ Zak Seidov, Jan 12 2016

Crossrefs

Cf. A104637, A159352.

Sequence in context: A323827 A275850 A112505 * A270648 A331034 A057155

Adjacent sequences: A104635 A104636 A104637 * A104639 A104640 A104641

Keyword

easy,nonn,base

Author

Zak Seidov, Mar 18 2005

Status

approved