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.

A097052 First occurrence of n in A096036 or 0 if n does not appear.

Original entry on oeis.org

1, 2, 5, 7, 19, 17, 25, 29, 0, 73, 65, 67, 99, 97, 113, 121, 0, 0, 301, 289, 0, 257, 265, 277, 393, 401, 421, 385, 451, 449, 481, 497, 0, 0, 0, 0, 0, 1201, 1161, 1153, 0, 0, 1025, 1033, 1059, 1057, 1105, 1129, 0, 1569, 1613, 1601, 1681, 1697, 1537, 1541, 1801, 1825
Offset: 1

Views

Author

Reinhard Zumkeller and Robert G. Wilson v, Jul 21 2004

Keywords

Comments

Not appearing in A096036 are 9, 17, 18, 21, 33, 34, 35, 36, 37, 41, 42, 49, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 81, 82, 83, 84, 85, 97, 98, 105, ...,.

Crossrefs

Cf. A096036.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = Ceiling[ n / a[ Ceiling[n/2]]]; t = Table[ a[n], {n, 2000}]; b[n_] := Block[{p = Position[t, n, 1, 1]}, If[p == {}, 0, p]]; Flatten[ Table[ b[n], {n, 60}]]

Formula

A096036: a(n)= ceiling(n/a(ceiling(n/2))) with a(1) = 1.

A097051 a(n) = floor(n/a(floor(n/2))); a(1) = 1.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller and Robert G. Wilson v, Jul 21 2004

Keywords

Examples

			a(50)=floor(50/a(25))
..... a(25)=floor(25/a(12))
........... a(12)=floor(12/a(6))
................. a(6)=floor(6/a(3))
...................... a(3)=floor(3/a(1))
........................... a(1)=1
...................... a(3)=floor(3/a(1))=floor(3/1)=3
................. a(6)=floor(6/a(3))=floor(6/3)=2
........... a(12)=floor(12/a(6))=floor(12/2)=6
..... a(25)=floor(25/a(12))=floor(25/6)=4
a(50)=floor(50/a(25))=floor(50/4)=12.

Links

Crossrefs

Cf. A096036, A097053.

Programs

  • Maple
    f:= proc(n) option remember;  floor(n/procname(floor(n/2))) end proc:
f(1):= 1:
map(f, [$1..200]); # Robert Israel, Jan 06 2021
  • Mathematica
    a[1] = 1; a[n_] := a[n] = Floor[n/a[Floor[n/2]]]; Table[ a[n], {n, 94}]

Formula

If floor(log_2(n))=2k+1, then a(n) = floor(n/2^k). If floor(log_2(n))=2k, then a(n) = 2^k.

Extensions

Formula added by Max Alekseyev, Mar 02 2011

A096038 Triangle T(n,m) = (3*n^2-3*m^2+5*m-4+n)/2 read by rows.

Original entry on oeis.org

1, 6, 4, 14, 12, 7, 25, 23, 18, 10, 39, 37, 32, 24, 13, 56, 54, 49, 41, 30, 16, 76, 74, 69, 61, 50, 36, 19, 99, 97, 92, 84, 73, 59, 42, 22, 125, 123, 118, 110, 99, 85, 68, 48, 25, 154, 152, 147, 139, 128, 114, 97, 77, 54, 28, 186, 184, 179, 171, 160, 146, 129, 109, 86, 60, 31
Offset: 1

Views

Author

Gary W. Adamson, Jun 17 2004

Keywords

Comments

The triangle is obtained by subtracting the triangle A094930 from
its square root (also described in A094930) and then dividing each element of column m through 3*m-1.
For the first three rows n=1 to 3 this yields for example:
4;.................2;............2......................1;
14,25;......minus..2,5;.......=..12,20;......->.divide..6,4;
30,65,64;..........2,5,8;........28,60,56;..............14;12,7;

Crossrefs

Cf. A095794, A011379, A002411, A096037, A096036, A024212.

Programs

  • Python
    def A096038(n,m):
    return (3*n**2-3*m**2+5*m-4+n)//2
print( [A096038(n,m) for n in range(20) for m in range(1,n+1)] )
# R. J. Mathar, Oct 11 2009

Formula

T(n,1) = A095794(n).
T(n,n) = 3*n-2.
T(n,m) = A094930(n,m)/(3*m-1)-1.

Extensions

Edited, T(3,2) corrected, and extended by R. J. Mathar, Oct 11 2009
Showing 1-3 of 3 results.

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