A096289 Sum of digits of n in bases 2 and 5.

0, 2, 3, 5, 5, 3, 4, 6, 5, 7, 4, 6, 6, 8, 9, 7, 5, 7, 8, 10, 6, 8, 9, 11, 10, 4, 5, 7, 7, 9, 6, 8, 5, 7, 8, 6, 6, 8, 9, 11, 6, 8, 9, 11, 11, 9, 10, 12, 10, 12, 5, 7, 7, 9, 10, 8, 7, 9, 10, 12, 8, 10, 11, 13, 9, 7, 8, 10, 10, 12, 9, 11, 10, 12, 13, 7, 7, 9, 10, 12, 6, 8, 9, 11, 11, 9, 10, 12, 11, 13

Offset: 0

Author

Miklos Kristof, Peter Boros, Jun 24 2004

Keywords

• easy
• nonn
• base

Comments

Let n = Sum(c(k)*2^k), c(k) = 0,1, be the binary form of n, n = Sum(d(k)*5^k), d(k) = 0,1,2,3,4 the base 5 form; then a(n) = Sum(c(k)+d(k)).

a(n) mod 2 = doubled Thue-Morse sequence A095190.

Examples

			n=13: 13=1*2^3+1*2^2+1*2^0, 1+1+1=3, 13=2*5^1+3*5^0, 2+3=5, so a(13)=3+5=8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000120, A010059, A010060, A053824, A095190, A096288.

Programs

Mathematica

a[n_] := Total[Flatten@ IntegerDigits[n, {2, 5}]]; Array[a, 100, 0] (* Amiram Eldar, Jul 28 2023 *)

Formula

a(n) = A000120(n) + A053824(n). - Amiram Eldar, Jul 28 2023