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 1-4 of 4 results.

A276335 Discard the most significant digit when n is expressed in greedy A001563-base (A276326), then convert back to decimal: a(n) = n - A276334(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 0
Offset: 0

Views

Author

Antti Karttunen, Aug 30 2016

Keywords

Links

Crossrefs

Cf. A001563, A276326, A276328, A276334, A276331, A276337.
Cf. also A257687.

Programs

  • Mathematica
    {0}~Join~Table[n - # Floor[n/#] &@(# #!) &@ NestWhile[# + 1 &, 0, # #! <= n &[# + 1] &], {n, 96}] (* Michael De Vlieger, Aug 31 2016 *)
  • Scheme
    (define (A276335 n) (- n (A276334 n)))

Formula

a(n) = n - A276334(n).

A258199 a(n) = largest term of A001563 <= n.

Original entry on oeis.org

0, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18
Offset: 0

Views

Author

Antti Karttunen, May 23 2015

Keywords

Links

Crossrefs

Cf. A001563, A258198, A256450, A276334.

Programs

  • Mathematica
    Table[# #! &@ NestWhile[# + 1 &, 0, # #! <= n &[# + 1] &], {n, 0, 96}] (* Michael De Vlieger, Aug 31 2016 *)

Formula

a(n) = A001563(A258198(n)).

A276333 The most significant digit in greedy A001563-base (A276326): a(n) = floor(n/A258199(n)), a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1
Offset: 0

Views

Author

Antti Karttunen, Aug 30 2016

Keywords

Links

Crossrefs

Cf. A001563, A276326, A258199, A276334, A276335.

Programs

  • Mathematica
    Table[Floor[n/(# #!)] &@ NestWhile[# + 1 &, 0, # #! <= n &[# + 1] &], {n, 96}] (* or *)
f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@#, Last@#} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@ NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; {0}~Join~Table[First@ f@ n, {n, 96}] (* Michael De Vlieger, Aug 31 2016 *)
  • Scheme
    (define (A276333 n) (if (zero? n) n (floor->exact (/ n (A258199 n)))))

Formula

a(0) = 0; for n >= 1, a(n) = floor(n/A258199(n)).

A276338 a(n) = A276333(n) * A001563(1+A258198(n)).

Original entry on oeis.org

0, 4, 8, 12, 18, 18, 18, 18, 36, 36, 36, 36, 54, 54, 54, 54, 72, 72, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 384
Offset: 0

Views

Author

Antti Karttunen, Sep 01 2016

Keywords

Comments

a(n) is obtained by first replacing with zeros all other digits except the leftmost (the most significant) in the greedy A001563-base representation of n (A276326), then appending an extra zero to the right, then converting back to decimal.
An auxiliary function for computing A276340.

Links

Crossrefs

Cf. A001563, A258198, A276326, A276333, A276334, A276340.

Programs

Formula

a(n) = A276333(n) * A001563(1+A258198(n)).
Other identities. For all n >= 0:
a(n) = A276340(A276334(n)).
Showing 1-4 of 4 results.

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