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

Author

Zak Seidov, Mar 18 2005

Keywords

• easy
• nonn
• base

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

Crossrefs

Cf. A104637, A159352.

Cf. A154764 (1 odd digit), A155071 (2 odd digits), A030096 (all digits odd).

Programs

Maple

seq(nops(select(type, convert(ithprime(i),base,10),odd)),i=1..100); # Robert Israel, Jan 12 2016
# alternative
A104638 := proc(n)
    local a,dgs,d ;
    ithprime(n) ;
    dgs := convert(%,base,10) ;
    a := 0 ;
    for d in dgs do
        a := a+modp(d,2) ;
    end do:
    a ;
end proc:
seq(A104638(n),n=1..40) ; # R. J. Mathar, Jul 13 2025

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 *)

PARI

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

Formula

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