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

1,2

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A031298.

Sequence in context: A081594 A038506 A091047 * A080719 A049105 A125959

Adjacent sequences: A068502 A068503 A068504 * A068506 A068507 A068508

Keyword

nonn,base,nice,look

Author

Reinhard Zumkeller, Mar 11 2002, Feb 23 2008

Extensions

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

Status

approved