A309735 a(n) is the least positive integer k such that k^n starts with 2.
2, 5, 3, 4, 3, 8, 3, 2, 4, 7, 2, 5, 9, 4, 9, 6, 7, 2, 4, 21, 2, 5, 7, 3, 5, 3, 8, 2, 4, 3, 2, 5, 11, 4, 5, 7, 8, 2, 6, 23, 2, 5, 6, 14, 3, 16, 3, 2, 3, 14, 2, 4, 15, 17, 5, 7, 4, 2, 11, 18, 2, 4, 47, 14, 5, 6, 4, 2, 7, 3, 2, 3, 13, 3, 5, 15, 4, 8, 6, 9, 2, 4, 11, 6, 5, 22, 4
Offset: 1
Examples
a(5) = 3 because 3^5 = 243 starts with 2, while 1^5=1 and 2^5=32 do not start with 2.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Magma
m:=1; sol:=[]; for n in [1..100] do k:=2; while Reverse(Intseq(k^n))[1] ne 2 do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // Marius A. Burtea, Aug 15 2019
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Maple
f:= proc(n) local x,y; for x from 2 do y:= x^n; if floor(y/10^ilog10(y)) = 2 then return x fi od end proc: map(f, [$1..100]); -
PARI
a(n) = for(k=1, oo, if(digits(k^n)[1]==2, return(k))) \\ Felix Fröhlich, Aug 14 2019
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Python
n = 1 while n < 100: k, s = 2, str(2**n) while s[0] != "2": k = k+1 s = str(k**n) print(n,k) n = n+1 # A.H.M. Smeets, Aug 14 2019
Comments