A362175 - OEIS

%I #39 Apr 14 2023 10:54:14

%S 32,46416,18,4,6813,2,75,6,2,152,6813,12,44,4,65,2,6,3,2,3,39,5,75,4,

%T 538,2,72,53,2,69,7,5,7627,4,6,2,12,13434,2,8,3,5,13,4,33246,2,14,11,

%U 2,18,538,5,6,152,75,2,7,21,2,3,552,3,75,3,39,2,3057,38,2,7,6,5

%N 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.

%H Jean-Marc Rebert, <a href="/A362175/b362175.txt">Table of n, a(n) for n = 3..1000</a>

%e 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.

%o (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

%o (Python)

%o from itertools import count

%o def a(n): return next(k for k in count(2) if (s:=str(k)).strip("0")!="1" and str(k**n).startswith(s))

%o print([a(n) for n in range(3, 75)]) # _Michael S. Branicky_, Apr 11 2023

%Y Cf. A100129, A362096, A320930, A362097, A362098, A362099, A362100, A362101.

%K nonn,base

%O 3,1

%A _Jean-Marc Rebert_, Apr 11 2023