A135102 Digital sum (base the n-th prime) of Fibonacci(n).

1, 1, 2, 3, 5, 8, 13, 3, 12, 27, 29, 36, 33, 41, 58, 51, 31, 64, 89, 45, 74, 83, 39, 168, 145, 193, 170, 129, 149, 104, 211, 289, 274, 175, 257, 252, 125, 161, 318, 347, 447, 316, 317, 285, 450, 107, 253, 648, 363, 301, 498, 409, 773, 522, 429, 515, 782, 649, 641

Offset: 1

Author

Hieronymus Fischer, Dec 24 2007

Keywords

• nonn
• base

Examples

			a(2) = ds_prime(2)(Fib(2)) = ds_3(1) = 1;
a(10) = ds_prime(10)(55) = ds_29(55) = 1+26 = 27.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000045, A007953, A054899, A075771, A131451, A133620, A133900, A134599.

Programs

Mathematica

Table[Total[IntegerDigits[Fibonacci[n],Prime[n]]],{n,60}] (* Harvey P. Dale, May 05 2013 *)

PARI

a(n) = vecsum(digits(fibonacci(n), prime(n))); \\ Michel Marcus, Sep 24 2016

Formula

a(n) = ds_prime(n)(Fib(n)), where ds_prime(n) = digital sum base the n-th prime.

a(n) = Fibonacci(n) - (prime(n)-1)*Sum{k>0} ( floor(Fibonacci(n)/prime(n)^k) ).