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A353138
Sum of (the number of digits in n to the power (each digit in n)).
1
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 6, 10, 18, 34, 66, 130, 258, 514, 5, 6, 8, 12, 20, 36, 68, 132, 260, 516, 9, 10, 12, 16, 24, 40, 72, 136, 264, 520, 17, 18, 20, 24, 32, 48, 80, 144, 272, 528, 33, 34, 36, 40, 48, 64, 96, 160, 288, 544, 65, 66, 68, 72, 80, 96
OFFSET
1,10
COMMENTS
In base 10, 1 and 4624 are the only numbers where a(n)=n (conjectured).
a(n) < n when n > 2.1*(10^10).
LINKS
FORMULA
a(n) = Sum_{k=1..A055642(n)} (A055642(n))^(floor(n*10^(1-k)) mod 10).
EXAMPLE
a(3) = 1^3 = 1;
a(164) = 3^1 + 3^6 + 3^4 = 813;
a(4624) = 4^4 + 4^6 + 4^2 + 4^4 = 4624.
MAPLE
f:= proc(n) local m, L, t;
L:= convert(n, base, 10);
m:= nops(L);
add(m^t, t=L)
end proc:
map(f, [$1..100]);
PROG
(Python)
def a(n): s = str(n); return sum(len(s)**int(d) for d in s)
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Apr 26 2022
(PARI) a(n) = my(d=digits(n)); vecsum(vector(#d, k, #d^d[k])); \\ Michel Marcus, Apr 27 2022
CROSSREFS
Sequence in context: A032408 A347567 A018908 * A052548 A232268 A103049
KEYWORD
nonn,look,base
AUTHOR
William Halpin, Apr 26 2022
STATUS
approved