A357143 - OEIS

%I #63 Oct 26 2023 20:17:21

%S 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,

%T 28,65,2,3,10,29,66,9,10,17,36,73,28,29,36,55,92,65,66,73,92,129,8,9,

%U 16,35,72,9,10,17,36,73,16,17,24,43,80,35,36,43,62,99,72,73,80,99,136,27

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

%H Robert Israel, <a href="/A357143/b357143.txt">Table of n, a(n) for n = 1..10000</a>

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

%e For n = 13_10 = 23_5 (2 digits in base 5): a(13) = 2^2 + 3^2 = 13.

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

%p f:= proc(n) local L,d,i;

%p   L:= convert(n,base,5);

%p   d:= nops(L);

%p   add(L[i]^d,i=1..d)

%p end proc:

%p map(f,[$1..100]); # _Robert Israel_, Oct 26 2023

%t a[n_] := Total[IntegerDigits[n, 5]^IntegerLength[n, 5]]; Array[a, 100] (* _Amiram Eldar_, Oct 30 2022 *)

%o (PARI) a(n) = my(d=digits(n, 5)); sum(k=1, #d, d[k]^#d); \\ _Michel Marcus_, Oct 29 2022

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o def A357143(n):

%o     t = len(s:=digits(n,5)[1:])

%o     return sum(d**t for d in s) # _Chai Wah Wu_, Oct 31 2022

%Y Cf. A357954, A010346, A110592.

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

%K nonn,base

%O 1,2

%A _Francesco A. Catalanotti_, Oct 26 2022

%E Corrected and extended by _Michel Marcus_, Oct 29 2022