cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A063013 Numbers where k-th digit from right is either 0 or k.

Original entry on oeis.org

0, 1, 20, 21, 300, 301, 320, 321, 4000, 4001, 4020, 4021, 4300, 4301, 4320, 4321, 50000, 50001, 50020, 50021, 50300, 50301, 50320, 50321, 54000, 54001, 54020, 54021, 54300, 54301, 54320, 54321, 600000, 600001, 600020, 600021, 600300, 600301, 600320, 600321
Offset: 0

Views

Author

Henry Bottomley, Jul 04 2001

Keywords

Comments

a(511) = 987654321 is the last term.

Examples

			 a(11) = 4021 since 11 is written as 1011 in binary and the 1's can then be replaced by the relevant digits.

Links

Crossrefs

Cf. A063012, A053541.

Programs

  • Maple
    a:= n-> (l-> parse(cat(seq(l[-i]*(1+nops(l)-i),
         i=1..nops(l)))))(convert(n, base, 2)):
seq(a(n), n=0..2^6-1);  # Alois P. Heinz, Oct 29 2018
  • Mathematica
    FromDigits /@ (Range[9,1,-1]*# & /@ IntegerDigits[Range[0, 511], 2, 9]) (* Giovanni Resta, Oct 28 2018 *)
  • PARI
    a(n) = fromdigits(Vec(Pol(binary(2*n))')); \\ Alan Michael Gómez Calderón, May 01 2025

Formula

a(n) = a(n-2^floor(log_2(n))) + floor(log_2(n)+1)*10^floor(log_2(n)).
a(n) = Sum_{k>=0} A030308(n,k)*A053541(k+1). - Philippe Deléham, Oct 15 2011

A302205 Let the binary expansion of n be [b_d, b_{d-1}, ..., b_3, b_2, b_1, b_0]_2, where (if n>0) b_d = 1, b_i = 0 or 1 for i

Original entry on oeis.org

0, 1, 20, 21, 400, 401, 420, 421, 8000, 8001, 8020, 8021, 8400, 8401, 8420, 8421, 160000, 160001, 160020, 160021, 160400, 160401, 160420, 160421, 168000, 168001, 168020, 168021, 168400, 168401, 168420, 168421, 3200000, 3200001, 3200020, 3200021, 3200400, 3200401, 3200420, 3200421, 3208000, 3208001, 3208020, 3208021, 3208400, 3208401, 3208420, 3208421, 32160000
Offset: 0

Views

Author

N. J. A. Sloane, Apr 26 2018

Keywords

Comments

First differs from A063012 (which uses base 20) at n = 48, where A063012(48) = 3360000, whereas here a(48) = 32160000.

Examples

			48_10 = 110000_2, so a(48) is the concatenation of 32, 16, 0, 0, 0, 0 = 32160000.

Crossrefs

Cf. A063012.

Extensions

More than the usual number of terms are displayed in order to distinguish this from A063012.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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