A242397 a(n) is the number of different bases b such that the Brazilian numbers A125134(n) remain a repdigit number.

1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 2, 2, 2, 2, 1, 1, 1, 3, 1, 1, 4, 3, 1, 2, 2, 1, 4, 2, 1, 2, 3, 1, 2, 2, 1, 5, 2, 4, 2, 1, 3, 2, 1, 3, 4, 1, 1, 2, 2, 1, 3, 5, 1, 1, 5, 2, 2, 1, 3, 4, 2, 2, 2, 1, 1, 5, 2, 2, 3, 3, 3, 3, 1, 5, 2, 2, 4, 4, 1, 2, 2, 1

Offset

1,7

Comments

For all numbers m, we restrict the bases b with 1 < b < m-1 because m is repdigit in bases 1 and also m-1.

Links

Michel Lagneau, Table of n, a(n) for n = 1..5000

Example

a(89) = 7 because A125134(89)=120 and the number 120 is AA in base 11 where A = 10, 88 in base 14, 66 in base 19, 55 in base 23, 44 in base 29, 33 in base 39 and 22 in base 59 => 7 representations.

Maple

for n from 1 to 200 do:c:=0:for b from 2 to n-2 do:x:=convert(n, base, b):n1:=nops(x):a:=x[n1]:i:=1:for k from n1-1 by -1 to 1 do:if x[k]=a then i:=i+1:else fi:od:if i=n1 then c:=c+1:i:=1:else fi:od:if c>0 then printf(`%d, `, c):else fi:od:

Crossrefs

Cf. A066460, A125134.

Sequence in context: A316384 A029838 A213649 * A023132 A023124 A023120

Adjacent sequences: A242394 A242395 A242396 * A242398 A242399 A242400

Keyword

nonn,base

Author

Michel Lagneau, May 13 2014

Status

approved