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URL: https://oeis.org/A104638

⇱ A104638 - OEIS

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A104638
Number of odd digits in n-th prime.
7
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
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
# 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 *)
PROG
(PARI) a(n)=vecsum(digits(prime(n)%2)) \\ Zak Seidov, Jan 12 2016
CROSSREFS
Cf. A154764 (1 odd digit), A155071 (2 odd digits), A030096 (all digits odd).
Sequence in context: A323827 A275850 A112505 * A270648 A331034 A057155
KEYWORD
easy,nonn,base
AUTHOR
Zak Seidov, Mar 18 2005
STATUS
approved