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.

A108870 a(n) = ceiling((9*(9/4)^n - 4) / 5).

Original entry on oeis.org

1, 4, 9, 20, 46, 103, 233, 525, 1182, 2660, 5985, 13467, 30301, 68178, 153401, 345152, 776591, 1747331, 3931496, 8845866, 19903198, 44782196, 100759940, 226709866, 510097200, 1147718700, 2582367076, 5810325920, 13073233321, 29414774973
Offset: 0

Views

Author

Jud McCranie, Jul 13 2005

Keywords

Comments

The old definition was "Tokuda's good set of increments for Shell sort", but that seems to be false.
Adding 0, -1, -1, -1, ... to the terms gives A361506. For another version see A361507.

References

  • N. Tokuda, An Improved Shellsort, IFIP Transactions, A-12 (1992) 449-457.

Links

Crossrefs

Other sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875, A055876, A361506, A361507.

Programs

Extensions

Edited by N. J. A. Sloane, Mar 20 2023 at the suggestion of Don Knuth.

A361507 a(0) = 1; thereafter a(n) = floor((9/4)*a(n-1)) + 1.

Original entry on oeis.org

1, 3, 7, 16, 37, 84, 190, 428, 964, 2170, 4883, 10987, 24721, 55623, 125152, 281593, 633585, 1425567, 3207526, 7216934, 16238102, 36535730, 82205393, 184962135, 416164804, 936370810, 2106834323, 4740377227, 10665848761, 23998159713, 53995859355, 121490683549, 273354037986, 615046585469, 1383854817306, 3113673338939
Offset: 0

Views

Author

N. J. A. Sloane, Mar 20 2023, following a suggestion from Don Knuth

Keywords

References

  • N. Tokuda, An efficient Shell's method of sorting by generalized scheme, Department of Computer Science, Utunomiya University, 1989; 10 pages plus 9 unnumbered pages of tables and charts.

Links

Crossrefs

Other sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875, A055876, A108870, A361506.

Programs

  • Mathematica
    NestList[Floor[9/4#]+1&,1,50] (* Paolo Xausa, Dec 02 2023 *)

A036567 Basic numbers used in Sedgewick-Incerpi upper bound for shell sort.

Original entry on oeis.org

1, 3, 7, 16, 41, 101, 247, 613, 1529, 3821, 9539, 23843, 59611, 149015, 372539, 931327, 2328307, 5820767, 14551919, 36379789, 90949471, 227373677, 568434193, 1421085473, 3552713687, 8881784201, 22204460497, 55511151233, 138777878081, 346944695197, 867361737989
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			2.5^4 = 39.0625, and 41 is the next integer that is relatively prime to 1, 3, 7 and 16.

References

  • D. E. Knuth, The Art of Computer Programming, Vol. 3, Sorting and Searching, 2nd ed, section 5.2.1, p. 91.

Links

Crossrefs

Cf. A003462, A033622, A036561, A036562, A036564, A036566, A036567, A036569, A055875, A055876, A102549, A108870, A112262, A112263, A154393, A204772, A205669, A205670, A361506, A361507.

Programs

  • Maple
    a:= proc(n) option remember; local l, m;
      l:= [seq(a(i), i=1..n-1)];
      for m from ceil((5/2)^n) while ormap(x-> igcd(m, x)>1, l) do od; m
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 06 2022
  • Mathematica
    A036567[1] = 3;
A036567[q_] :=
With[{prev = A036567 /@ Range[q - 1]},
  Block[{n = Ceiling[(5/2)^q]},
   While[Nand @@ ((# == 1 &) /@ GCD[prev, n]), n++];
   n]]; (* Morgan Owens, Oct 08 2020 *)
Array[A036567, 10]
  • PARI
    a036567(m)={my(v=vector(m)); for(n=1,m,my(b=ceil((5/2)^n));for(j=b,oo,my(g=1); for(k=1,n-1,if(gcd(j,v[k])>1,g=0;break));if(g,v[n]=j;break)));v};
a036567(28) \\ Hugo Pfoertner, Oct 15 2020

Formula

a(n) is the smallest number >= 2.5^n that is relatively prime to all previous terms in the sequence.

Extensions

Better description and more terms from Jud McCranie, Jan 05 2001
a(0)=1 prepended by Alois P. Heinz, Dec 04 2023
Showing 1-3 of 3 results.

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

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