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

1,2

Links

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

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.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A357954, A010346, A110592.

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

Sequence in context: A074057 A299756 A163258 * A337210 A361258 A141063

Adjacent sequences: A357140 A357141 A357142 * A357144 A357145 A357146

Keyword

nonn,base

Author

Francesco A. Catalanotti, Oct 26 2022

Extensions

Corrected and extended by Michel Marcus, Oct 29 2022

Status

approved