A097251 Numbers whose set of base 5 digits is {0,4}.

0, 4, 20, 24, 100, 104, 120, 124, 500, 504, 520, 524, 600, 604, 620, 624, 2500, 2504, 2520, 2524, 2600, 2604, 2620, 2624, 3000, 3004, 3020, 3024, 3100, 3104, 3120, 3124, 12500, 12504, 12520, 12524, 12600, 12604, 12620, 12624, 13000, 13004, 13020

Offset: 0

Author

Ray Chandler, Aug 03 2004

Keywords

• nonn
• base

Comments

n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 5 for every i.

The first 2^n terms of the sequence could be obtained using the Cantor-like process for the segment [0,5^n-1]. For example, for n=1 we have [0, {1,2,3},4] such that numbers outside of braces are the first 2 terms of the sequence; for n=2 we have [0, {1,2,3}, 4, {5,...,19}, 20, {21,22,23}, 24] such that the numbers outside of braces are the first 4 terms of the sequence, etc. - Vladimir Shevelev, Dec 17 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001196, A005823, A097252-A097262.

Programs

Magma

[n: n in [0..20000] | Set(IntegerToSequence(n, 5)) subset {0, 4}]; // Vincenzo Librandi, May 25 2012

Mathematica

fQ[n_]:=Union@Join[{0,4},IntegerDigits[n,5]]=={0,4};Select[Range[0,20000],fQ] (* Vincenzo Librandi, May 25 2012 *)
FromDigits[#,5]&/@Tuples[{0,4},6] (* Harvey P. Dale, Feb 01 2015 *)

Maxima

a[0]:0$ a[n]:=5*a[floor(n/2)]+2*(1-(-1)^n)$ makelist(a[n], n, 0, 42); /* Bruno Berselli, May 25 2012 */

PARI

a(n) = 4*fromdigits(binary(n),5); \\ Kevin Ryde, Jun 03 2020

Formula

a(n) = 4*A033042(n).

a(2n) = 5*a(n), a(2n+1) = a(2n)+4.