

A118716


Number of different ways to represent n in different bases using only decimal digits or characters (0 to 9).


2



1, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 28, 29, 30, 29, 29, 31, 30, 30, 31, 31, 31, 31, 31, 32, 33, 31, 31, 34, 33, 32, 33, 33, 33, 34, 33, 34, 35, 33, 33, 36
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OFFSET

1,2


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Base.


EXAMPLE

a(27) = 23 because the representation of 27 in unary, binary, ternary, quaternary, etc... bases is as follows: 111111111111111111111111111, 11011, 1000, 123, 102, 43, 36, 33, 30, 27, 25, 23, 21, 1D, 1C, 1B, 1A, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, R, R, R, R..... etc.
Of all of these representations, 23 of them contain only decimal digits (or characters).


MAPLE

N:= 1000: # to get a(1)..a(N)
A:= Vector(N, 1):
A[1]:= 0:
for b from 2 to N do
d:= ilog[b](N);
S:= {$1..9}:
for i from 1 to d do
S:= S union map(t > seq(b*t+j, j=0..9), S);
od:
S:= convert(select(t > (t<=N and t >= b1), S), list);
A[S]:= map(`+`, A[S], 1);
od:
convert(A, list); # Robert Israel, Jun 14 2016


MATHEMATICA

f[n_] := 1 + If[n == 1, 0, Length@Select[Table[IntegerDigits[n, b], {b, 2, n + 1}], Apply[And, Map[ # < 10 &, # ]] &]]; Table[f[n], {n, 72}] (*Chandler*)


CROSSREFS

Cf. A095425, A095426, A095427, A095428, A095429, A095430, A095431, A095432, A095433.
Sequence in context: A243196 A247485 A154781 * A004177 A004721 A030544
Adjacent sequences: A118713 A118714 A118715 * A118717 A118718 A118719


KEYWORD

base,nonn


AUTHOR

Sergio Pimentel, May 24 2006


EXTENSIONS

Corrected by Ray Chandler, Jun 19 2006


STATUS

approved



