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

3,1

Links

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

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

Crossrefs

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

Sequence in context: A320859 A285389 A159396 * A221086 A054374 A221138

Adjacent sequences: A362172 A362173 A362174 * A362176 A362177 A362178

Keyword

nonn,base

Author

Jean-Marc Rebert, Apr 11 2023

Status

approved