A156607 a(n) = number of odd decimal digits of n-th prime + number of prime decimal digits of n-th prime.

1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 4, 1, 2, 2, 4, 3, 1, 2, 3, 4, 3, 2, 1, 3, 2, 3, 3, 2, 4, 4, 4, 5, 4, 2, 4, 5, 3, 3, 5, 4, 2, 3, 4, 4, 3, 3, 4, 4, 3, 5, 4, 2, 4, 5, 3, 2, 4, 5, 2, 3, 4, 4, 4, 5, 5, 5, 6, 4, 3, 6, 5, 4, 6, 5, 4, 3, 5, 1, 1, 2, 2, 3, 4, 3, 2, 1, 4, 1, 2, 2, 3, 2, 2, 2, 4, 3, 4, 5, 3, 4, 6, 4, 3, 5

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 11 2009

Keywords

• nonn
• base

Comments

Odd digits are 1, 3, 5, 7 and 9. Prime digits are 2, 3, 5 and 7.

Examples

			prime(1)= 2 (0 odd digits, 1 prime), so a(1) = 0 + 1 = 1;
prime(2)= 3 (1 odd digit,  1 prime), so a(2) = 1 + 1 = 2;
prime(3)= 5 (1 odd digit,  1 prime), so a(3) = 1 + 1 = 2;
prime(4)= 7 (1 odd digit,  1 prime), so a(4) = 1 + 1 = 2;
prime(5)=11 (2 odd digits, 0 prime), so a(5) = 2 + 0 = 2;
prime(6)=13 (2 odd digits, 1 prime), so a(6) = 2 + 1 = 3.
		

Crossrefs

Cf. A000040, A104638.

Programs

Maple

numPdgs := proc(n) local f,d ; f := 0 ; for d in convert(n,base,10) do if d in {2,3,5,7} then f :=f+1; end if; end do; f ; end proc:
numOdddgs := proc(n) local f,d ; f := 0 ; for d in convert(n,base,10) do if type(d,'odd') then f :=f+1; end if; end do; f ; end proc:
A156607 := proc(n) p := ithprime(n) ; numPdgs(p) + numOdddgs(p) ; end proc:
seq(A156607(n),n=1..120) ; # R. J. Mathar, May 15 2010

Mathematica

d[n_]:=Module[{idn=IntegerDigits[n]},Count[idn,?OddQ]+Count[ idn, ?PrimeQ]]; d/@Prime[Range[150]] (* Harvey P. Dale, May 16 2014 *)

Extensions

a(54) corrected by R. J. Mathar, May 15 2010

Example section edited by Jon E. Schoenfield, Feb 14 2019