cp's OEIS Frontend

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.

%I A362175 #39 Apr 14 2023 10:54:14
%S A362175 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 A362175 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 A362175 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 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.
%H A362175 Jean-Marc Rebert, <a href="/A362175/b362175.txt">Table of n, a(n) for n = 3..1000</a>
%e A362175 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 A362175 (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 A362175 (Python)
%o A362175 from itertools import count
%o A362175 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 A362175 print([a(n) for n in range(3, 75)]) # _Michael S. Branicky_, Apr 11 2023
%Y A362175 Cf. A100129, A362096, A320930, A362097, A362098, A362099, A362100, A362101.
%K A362175 nonn,base
%O A362175 3,1
%A A362175 _Jean-Marc Rebert_, Apr 11 2023