A091837 Smallest b>1 such that 11*n is a repdigit in base b.

10, 10, 10, 10, 10, 10, 10, 10, 10, 21, 3, 21, 12, 13, 14, 15, 16, 17, 18, 19, 20, 3, 22, 21, 24, 21, 26, 21, 28, 21, 4, 21, 32, 21, 34, 21, 36, 21, 32, 21, 40, 32, 42, 43, 32, 45, 46, 23, 48, 24, 32, 25, 52, 26, 54, 27, 32, 28, 58, 29, 60, 4, 32, 31, 54, 32, 66, 33, 32

Offset

1,1

Comments

a(n) <= n-1 for n >= 12. - Robert Israel, Apr 13 2021

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Eric Weisstein's World of Mathematics, Repdigit

Example

n=11: 121=11*11 in binary = '1111001', but in ternary = '11111', therefore a(11)=3;
n=93: 1023=11*93 in binary = '1111111111', therefore a(93)=2.

Maple

f:= proc(n) local b, d, m;
      for b from 2 do
        d:= (11*n) mod b;
        m:= ceil(log[b](11*n));
        if 11*n = d*(b^m-1)/(b-1) then return b fi
      od
end proc:
map(f, [$1..100]); # Robert Israel, Apr 13 2021

Crossrefs

Cf. A008593.

Sequence in context: A070565 A169932 A245403 * A316650 A216875 A166710

Adjacent sequences: A091834 A091835 A091836 * A091838 A091839 A091840

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Mar 10 2004

Status

approved