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URL: https://oeis.org/A362175

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A362175
Least number k > 1 not a power of 10 such that k^n, n > 2, starts with k, or -1 if no such number exists.
1
32, 46416, 18, 4, 6813, 2, 75, 6, 2, 152, 6813, 12, 44, 4, 65, 2, 6, 3, 2, 3, 39, 5, 75, 4, 538, 2, 72, 53, 2, 69, 7, 5, 7627, 4, 6, 2, 12, 13434, 2, 8, 3, 5, 13, 4, 33246, 2, 14, 11, 2, 18, 538, 5, 6, 152, 75, 2, 7, 21, 2, 3, 552, 3, 75, 3, 39, 2, 3057, 38, 2, 7, 6, 5
OFFSET
3,1
LINKS
EXAMPLE
a(3) = 32, because 32^3 = 32768 begins with 32, and no lesser number k > 2 and not a power of 10 has this property.
PROG
(PARI) a(n) = my(k=2); while(!((v = strsplit(Str(k^n), Str(k))) && (#v >= 2) && (v[1] == "")), k++; if (sumdigits(k)==1, k++)); k; \\ Michel Marcus, Apr 11 2023
(Python)
from itertools import count
def a(n): return next(k for k in count(2) if (s:=str(k)).strip("0")!="1" and str(k**n).startswith(s))
print([a(n) for n in range(3, 75)]) # Michael S. Branicky, Apr 11 2023
KEYWORD
nonn,base
AUTHOR
Jean-Marc Rebert, Apr 11 2023
STATUS
approved