A357143 a(n) is sum of the base-5 digits of n each raised to the number of digits of n in base 5.

1, 2, 3, 4, 1, 2, 5, 10, 17, 4, 5, 8, 13, 20, 9, 10, 13, 18, 25, 16, 17, 20, 25, 32, 1, 2, 9, 28, 65, 2, 3, 10, 29, 66, 9, 10, 17, 36, 73, 28, 29, 36, 55, 92, 65, 66, 73, 92, 129, 8, 9, 16, 35, 72, 9, 10, 17, 36, 73, 16, 17, 24, 43, 80, 35, 36, 43, 62, 99, 72, 73, 80, 99, 136, 27

Offset: 1

Author

Francesco A. Catalanotti, Oct 26 2022

Keywords

• nonn
• base

Examples

			For n = 13_10 = 23_5 (2 digits in base 5): a(13) = 2^2 + 3^2 = 13.
For n = 73_10 = 243_5 (3 digits in base 5): a(73) = 2^3 + 4^3 + 3^3 = 99.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A357954, A010346, A110592.

Cf. in base 10: A157714, A101337, A151544.

Programs

Maple

f:= proc(n) local L,d,i;
  L:= convert(n,base,5);
  d:= nops(L);
  add(L[i]^d,i=1..d)
end proc:
map(f,[$1..100]); # Robert Israel, Oct 26 2023

Mathematica

a[n_] := Total[IntegerDigits[n, 5]^IntegerLength[n, 5]]; Array[a, 100] (* Amiram Eldar, Oct 30 2022 *)

PARI

a(n) = my(d=digits(n, 5)); sum(k=1, #d, d[k]^#d); \\ Michel Marcus, Oct 29 2022

Python

from sympy.ntheory.factor_ import digits
def A357143(n):
    t = len(s:=digits(n,5)[1:])
    return sum(d**t for d in s) # Chai Wah Wu, Oct 31 2022

Formula

a(n) = Sum_{i=1..A110592(n)} d(i)^A110592(n), where d(i) is the i-th digit of n in base 5.

Extensions

Corrected and extended by Michel Marcus, Oct 29 2022