A068505 Decimal representation of n interpreted in base b+1, where b=A054055(n) is the largest digit in decimal representation of n.

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, 29, 12, 13, 14, 15, 19, 23, 27, 31, 35, 39, 20, 21, 22, 23, 24, 29, 34, 39, 44, 49, 30, 31, 32, 33, 34, 35, 41, 47, 53, 59, 42, 43, 44, 45, 46, 47, 48, 55, 62, 69, 56, 57, 58, 59, 60, 61

Offset: 1

Author

Reinhard Zumkeller, Mar 11 2002, Feb 23 2008

Keywords

• nonn
• base
• nice
• look

Comments

a(n) = n iff n < 10 OR n is a "9ish number": a(A011539(n)) = A011539(n). - Reinhard Zumkeller, Dec 29 2011

Examples

			a(20)=2*3^1+0*1=6, a(21)=2*3^1+1*1=7, a(22)=2*3^1+2*1=8,
a(23)=2*4^1+3*1=11, a(24)=2*5^1+4*1=14, a(25)=2*6^1+5*1=17,
a(26)=2*7^1+6*1=20, a(27)=2*8^1+7*1=23, a(28)=2*9^1+8*1=26,
a(29)=2*10^1+9*1=29, a(30)=3*4^1+0*1=12, a(31)=3*4^1+1*1=13.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..11000

Crossrefs

Cf. A031298.

Programs

Haskell

a068505 n = foldr (\d v -> v * b + d) 0 dds where
b = maximum dds + 1
dds = a031298_row n
-- Reinhard Zumkeller, Feb 17 2013, Dec 29 2011

Maple

f:= proc(n) local b,L,i;
L:= convert(n,base,10);
b:= max(L);
add(L[i]*(b+1)^(i-1),i=1..nops(L));
end proc:
map(f, [$1..100]); # Robert Israel, Feb 02 2016

Mathematica

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 *)
Table[FromDigits[IntegerDigits[n],Max[IntegerDigits[n]+1]],{n,80}] (* Harvey P. Dale, Dec 02 2015 *)

PARI

a(n)=my(d = digits(n), b = vecmax(d)); subst(Pol(d), x, b+1); \\ Michel Marcus, Feb 12 2016

Extensions

Definition clarified and comment corrected by Martin Büttner, Feb 02 2016