A068505 - OEIS

%I #29 Feb 13 2017 02:02:50

%S 1,2,3,4,5,6,7,8,9,2,3,5,7,9,11,13,15,17,19,6,7,8,11,14,17,20,23,26,

%T 29,12,13,14,15,19,23,27,31,35,39,20,21,22,23,24,29,34,39,44,49,30,31,

%U 32,33,34,35,41,47,53,59,42,43,44,45,46,47,48,55,62,69,56,57,58,59,60,61

%N Decimal representation of n interpreted in base b+1, where b=A054055(n) is the largest digit in decimal representation of n.

%C a(n) = n iff n < 10 OR n is a "9ish number": a(A011539(n)) = A011539(n). - _Reinhard Zumkeller_, Dec 29 2011

%H R. Zumkeller, <a href="/A068505/b068505.txt">Table of n, a(n) for n = 1..11000</a>

%e a(20)=2*3^1+0*1=6, a(21)=2*3^1+1*1=7, a(22)=2*3^1+2*1=8,

%e a(23)=2*4^1+3*1=11, a(24)=2*5^1+4*1=14, a(25)=2*6^1+5*1=17,

%e a(26)=2*7^1+6*1=20, a(27)=2*8^1+7*1=23, a(28)=2*9^1+8*1=26,

%e a(29)=2*10^1+9*1=29, a(30)=3*4^1+0*1=12, a(31)=3*4^1+1*1=13.

%p f:= proc(n) local b,L,i;

%p L:= convert(n,base,10);

%p b:= max(L);

%p add(L[i]*(b+1)^(i-1),i=1..nops(L));

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Feb 02 2016

%t a[n_] := (id = IntegerDigits[n] // Reverse; b = Max[id]+1; id.b^Range[0, Length[id]-1]); Table[a[n], {n, 1, 75}] (* _Jean-François Alcover_, May 15 2013 *)

%t Table[FromDigits[IntegerDigits[n],Max[IntegerDigits[n]+1]],{n,80}] (* _Harvey P. Dale_, Dec 02 2015 *)

%o (Haskell)

%o a068505 n = foldr (\d v -> v * b + d) 0 dds where

%o b = maximum dds + 1

%o dds = a031298_row n

%o -- _Reinhard Zumkeller_, Feb 17 2013, Dec 29 2011

%o (PARI) a(n)=my(d = digits(n), b = vecmax(d)); subst(Pol(d), x, b+1); \\ _Michel Marcus_, Feb 12 2016

%Y Cf. A031298.

%K nonn,base,nice,look

%O 1,2

%A _Reinhard Zumkeller_, Mar 11 2002, Feb 23 2008

%E Definition clarified and comment corrected by _Martin Büttner_, Feb 02 2016