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

Author

Michel Lagneau, May 13 2014

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A066460, A125134.

Programs

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: