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.

Showing 1-3 of 3 results.

A219651 a(n) = n minus (sum of digits in factorial base expansion of n).

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 5, 5, 6, 6, 7, 7, 10, 10, 11, 11, 12, 12, 15, 15, 16, 16, 17, 17, 23, 23, 24, 24, 25, 25, 28, 28, 29, 29, 30, 30, 33, 33, 34, 34, 35, 35, 38, 38, 39, 39, 40, 40, 46, 46, 47, 47, 48, 48, 51, 51, 52, 52, 53, 53, 56, 56, 57, 57, 58, 58, 61, 61
Offset: 0

Views

Author

Antti Karttunen, Nov 25 2012

Keywords

Comments

See A007623 for the factorial base number system representation.

Crossrefs

Bisection: A219650. Analogous sequence for binary system: A011371, for Zeckendorf expansion: A219641.

Programs

  • Mathematica
    (* First run program for A007623 to define factBaseIntDs *) Table[n - Plus@@factBaseIntDs[n], {n, 0, 99}] (* Alonso del Arte, Nov 25 2012 *)
  • Python
    from itertools import count
    def A219651(n):
        c, f = 0, 1
        for i in count(2):
            f *= i
            if f>n:
                break
            c += (i-1)*(n//f)
        return c # Chai Wah Wu, Oct 11 2024
  • Scheme
    (define (A219651 n) (- n (A034968 n)))
    

Formula

a(n) = n - A034968(n).

A219657 Positions of zeros in A219659.

Original entry on oeis.org

0, 2, 5, 8, 12, 16, 21, 26, 32, 38, 44, 50, 57, 64, 71, 78, 86, 94, 102, 110, 119, 128, 137, 146, 156, 166, 177, 188, 199, 210, 222, 234, 246, 258, 271, 284, 297, 310, 324, 338, 352, 366, 381, 396, 411, 426, 441, 456, 472, 488, 504, 520, 537, 554, 571, 588, 606
Offset: 0

Views

Author

Antti Karttunen, Nov 25 2012

Keywords

Crossrefs

Cf. A219656, A219659. Analogous sequence for binary system: A213707, for Zeckendorf expansion: A219647.

Programs

Formula

a(n) = n + A219656(n).

A219646 Partial sums of A219642.

Original entry on oeis.org

0, 1, 3, 6, 9, 13, 17, 22, 28, 34, 41, 48, 55, 63, 71, 80, 89, 98, 108, 118, 128, 139, 150, 162, 174, 186, 199, 212, 225, 239, 253, 267, 282, 297, 313, 329, 346, 363, 380, 398, 416, 434, 453, 472, 491, 511, 531, 552, 573, 594, 616, 638, 660, 682, 705, 729, 753
Offset: 0

Views

Author

Antti Karttunen, Nov 24 2012

Keywords

Crossrefs

Used to compute A219647. Analogous sequence for binary system: A213706, for factorial number system: A219656.
Showing 1-3 of 3 results.