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.
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
Examples
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.
Links
- Jean-Marc Rebert, Table of n, a(n) for n = 3..1000
Programs
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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
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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