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A309707 a(n) is the least integer k > 1 such that k^n starts with 1. 2
10, 4, 5, 2, 4, 5, 2, 6, 3, 2, 3, 4, 3, 2, 3, 5, 2, 6, 3, 2, 3, 4, 5, 2, 4, 5, 2, 8, 5, 2, 6, 3, 5, 2, 4, 3, 2, 3, 5, 2, 8, 3, 5, 2, 4, 5, 2, 10, 5, 2, 7, 10, 3, 2, 3, 5, 2, 6, 3, 2, 3, 6, 3, 2, 3, 5, 2, 10, 5, 2, 6, 6, 5, 2, 4, 3, 2, 3, 5, 2, 6, 3, 5, 2, 4, 3, 2, 10, 5, 2, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

1 <= a(n) <= 10.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A067442(n)^(1/n) for n >= 2.

EXAMPLE

a(3)=5 because 5^3=125 starts with 1, and none of 2^3, 3^3, 4^3 do.

MAPLE

f:= proc(n) local d, x, y;

  for x from 2 to 10 do

    y:= x^n;

    if floor(y/10^ilog10(y)) = 1 then return x fi

od

end proc:

map(f, [$1..100]);

PROG

(MAGMA) m:=1; sol:=[]; for n in [1..100] do k:=2; while Reverse(Intseq(k^n))[1] ne 1 do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // Marius A. Burtea, Aug 15 2019

(PARI) a(n) = {my(k=2); while(digits(k^n)[1] != 1, k++); k; } \\ Michel Marcus, Aug 15 2019

(Python)

print(1, 10)

n = 1

while n < 100:

    n, p = n+1, 2

    s = str(p**n)

    while s[0] != "1":

        p = p+1

        s = str(p**n)

    print(n, p) # A.H.M. Smeets, Aug 16 2019

CROSSREFS

Cf. A067442.

Sequence in context: A063566 A153690 A018811 * A100844 A076587 A266999

Adjacent sequences:  A309704 A309705 A309706 * A309708 A309709 A309710

KEYWORD

nonn,base

AUTHOR

Robert Israel, Aug 13 2019

STATUS

approved

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Last modified October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)