A030102 Base-3 reversal of n (written in base 10).

0, 1, 2, 1, 4, 7, 2, 5, 8, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• look
• easy

Examples

			a(17) = 25 because 17 in base 3 is 122, and backwards that is 221, which is 25 in base 10.
a(18) = 2 because 18 in base 3 is 200, and backwards that is 2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Michael Gilleland, Some Self-Similar Integer Sequences
• Lukas Spiegelhofer, A digit reversal property for an analogue of Stern's sequence, arXiv:1709.05651 [math.NT], 2017. See Theorem 1.1.

Crossrefs

Cf. A134028, A030101 - A030108, A004086, A134028.

Cf. A030341.

Cf. A263273 for a bijective variant.

Programs

Haskell

a030102 = foldl (\v d -> 3 * v + d) 0 . a030341_row
-- Reinhard Zumkeller, Dec 16 2013

Maple

a030102:= proc(n) option remember;
  local y;
  y:= n mod 3;
  3^ilog[3](n)*y + procname((n-y)/3)
end proc:
for i from 0 to 2 do a030102(i):= i od:
seq(a030102(i),i=0..100); # Robert Israel, Dec 24 2015
# alternative
A030102 := proc(n)
    local r ;
    r := ListTools[Reverse](convert(n,base,3)) ;
    add(op(i,r)*3^(i-1),i=1..nops(r)) ;
end proc: # R. J. Mathar, May 28 2016

Mathematica

A030102[n_] := FromDigits[Reverse@IntegerDigits[n, 3], 3] (* JungHwan Min, Dec 23 2015 *)
FromDigits[#,3]&/@(Reverse/@IntegerDigits[Range[0,80],3]) (* Harvey P. Dale, Feb 05 2020 *)

PARI

a(n,b=3)=subst(Polrev(base(n,b)),x,b) /* where */
base(n,b)={my(a=[n%b]);while(0M. F. Hasler, Nov 04 2011

PARI

a(n) = fromdigits(Vecrev(digits(n, 3)), 3); \\ Michel Marcus, Oct 10 2017

Formula

a(n) = t(n,0) with t(n,r) = if n=0 then r else t(floor(n/3),r*3+(n mod 3)). - Reinhard Zumkeller, Mar 04 2010

G.f. G(x) satisfies: G(x) = (1+x+x^2)*G(x^3) - (1+2*x)*(x + 2*Sum_{m>=0} 3^m*x^(3^(m+1)+1)/(x^3-1). - Robert Israel, Dec 24 2015