A389091 Sum over i of the i-th digit of n raised to the i-th power.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 2, 3, 6, 11, 18, 27, 38, 51, 66, 83, 3, 4, 7, 12, 19, 28, 39, 52, 67, 84, 4, 5, 8, 13, 20, 29, 40, 53, 68, 85, 5, 6, 9, 14, 21, 30, 41, 54, 69, 86, 6, 7, 10, 15, 22, 31, 42, 55, 70, 87, 7, 8, 11, 16, 23, 32, 43, 56, 71, 88, 8, 9, 12, 17, 24, 33

Offset

0,3

Comments

Let n have digits d_1...d_m. Then a(n) = d_1^1 + d_2^2 + ... + d_m^m.

Links

Table of n, a(n) for n=0..85.

Formula

a(n) = d_1^1 + d_2^2 + ... + d_m^m.

Example

a(0) = 0^1 = 0.
a(16) = 1^1 + 6^2 = 37.
a(234) = 2^1 + 3^2 + 4^3 = 75.
a(1001) = 1^1 + 0^2 + 0^3 + 1^4 = 2.

Mathematica

a[n_] := Module[{d = IntegerDigits[n]}, Total[d^Range[Length[d]]]]; Array[a, 100, 0] (* Amiram Eldar, Oct 23 2025 *)

Prog

(MATLAB)
a = @(k) sum((num2str(k)-'0').^(1:length(num2str(k))));
arrayfun(a, 0:100)
(Python)
def a(n): return sum(d**i for i, d in enumerate(map(int, str(n)), 1))
print([a(n) for n in range(86)]) # Michael S. Branicky, Oct 23 2025
(PARI) a(n) = my(d=digits(n)); sum(k=1, #d, d[k]^k); \\ Michel Marcus, Oct 25 2025

Crossrefs

Cf. A032799 (fixed points), A101337.

Sequence in context: A340270 A115026 A360075 * A101337 A135208 A259043

Adjacent sequences: A389088 A389089 A389090 * A389092 A389093 A389094

Keyword

nonn,base,easy

Author

Safwan Jaradat, Oct 23 2025

Status

approved