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.

A122805 A122804(n)/n.

Original entry on oeis.org

1, 2, 1, 3, 2, 2, 3, 4, 1, 4, 5, 4, 2, 2, 3, 7, 1, 6, 6, 9, 3, 6, 1, 7, 6, 4, 10, 1, 5, 5, 6, 4, 3, 5, 2, 7, 10, 7, 1, 10, 8, 6, 7, 8, 11, 2, 4, 12, 5, 3, 8, 9, 2, 9, 3, 14, 6, 7, 11, 13, 8, 16, 4, 2, 11, 14, 11, 6, 6, 1, 10, 12, 9, 21, 2, 13, 5, 6, 8, 15, 6, 4, 7, 3, 2, 9, 10, 16, 12, 13, 17, 1, 5, 12
Offset: 1

Views

Author

Ray Chandler, Sep 23 2006

Keywords

Links

A122806 Numbers not in A122804.

Original entry on oeis.org

2, 5, 6, 7, 8, 11, 13, 14, 15, 16, 18, 19, 20, 22, 24, 25, 27, 29, 30, 31, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90
Offset: 1

Views

Author

Ray Chandler, Sep 23 2006

Keywords

A122544 Smallest positive number divisible by n which is not of the form a(i) or a(i)+a(j) for i and j <= n-1.

Original entry on oeis.org

1, 4, 3, 12, 10, 18, 35, 32, 9, 40, 55, 48, 26, 84, 105, 112, 17, 54, 76, 100, 231, 198, 23, 120, 25, 156, 162, 280, 203, 150, 31, 192, 264, 68, 245, 288, 222, 418, 468, 440, 82, 294, 301, 352, 405, 368, 141, 432, 98, 600, 714, 520, 424, 702, 275, 672, 513, 928, 177
Offset: 1

Views

Author

N. J. A. Sloane, Sep 20 2006

Keywords

Comments

Same as A122537, except that a(n) is allowed to be less than a(n-1) (but not equal to it, or any other previous term).

Links

Crossrefs

Cf. A122537, A122545 (a(n)/n), A122546 (complement), A122804.

Programs

  • Maple
    a:=array(0..100000); m:=array(0..100000); hit:=array(0..100000); B:=100000; M:=120;
for n from 1 to B do hit[n]:=0; od:
a[1]:=1; m[1]:=1; a[2]:=4; m[2]:=2; hit[2]:=1; hit[5]:=1; hit[8]:=1; hit[1]:=1; hit[4]:=1;
for n from 3 to M do i:=n; while hit[i] = 1 do i:=i+n; od; a[n]:= i; m[n]:= i/n; hit[i]:=1;
for j from 1 to n do hit[a[j]+i]:=1; od; od:
t1:=[seq(a[n],n=1..M)]; t2:=[seq(m[n],n=1..M)];
  • Mathematica
    f[s_] := Block[{n, k},k = n = Length[s] + 1;While[MemberQ[Union[s, Plus @@@ Tuples[s, 2]], k], k += n];Append[s, k]];Nest[f, {1}, 60] (* Ray Chandler, Sep 29 2006 *)

A122537 a(1) = 1; for n>1, a(n) is smallest number greater than a(n-1), divisible by n and not equal to any a(i)+a(j) with i and j <= n-1.

Original entry on oeis.org

1, 4, 6, 16, 25, 30, 35, 40, 45, 100, 110, 120, 143, 154, 180, 192, 204, 216, 228, 260, 294, 330, 345, 480, 500, 572, 594, 616, 638, 720, 744, 768, 858, 884, 945, 1008, 1036, 1102, 1131, 1160, 1189, 1218, 1247, 1320, 1395, 1426, 1457, 1584, 1617, 1700, 1734
Offset: 1

Views

Author

J. Lowell, Sep 18 2006

Keywords

Comments

The definition: "a(1) = 1; for n>1, a(n) is smallest number greater than a(n-1) and not equal to any a(i)+a(j) with i and j <= n-1" produces the odd numbers 1, 3, 5, ...
Jonathan Vos Post asks if 1, 2, 4 and 5 are the only values of n for which n^2 divides a(n), Sep 19 2006. J. Lowell, Oct 02 2006 remarks that n = 1, 2, 4, 5 and 10 have this property and conjectures that there are no other values.

Examples

			The 5th term cannot be 20 because 20 = 16+4 and 16 and 4 are both in the sequence.

Crossrefs

Cf. A122543 (a(n)/n), A002858, A122544, A122545, A122804.

Programs

  • Maple
    # a[n] = n-th term of sequence, m[n] = a[n]/n = A122543(n) (Maple program from N. J. A. Sloane)
a:=array(0..100000); m:=array(0..100000); hit:=array(0..100000); B:=100000; M:=100;
for n from 1 to B do hit[n]:=0; od:
a[1]:=1; m[1]:=1; a[2]:=4; m[2]:=2; hit[2]:=1; hit[5]:=1; hit[8]:=1;
for n from 3 to M do i:=n*(floor(a[n-1]/n))+n;
while hit[i] = 1 do i:=i+n; od;
a[n]:= i; m[n]:= i/n;
for j from 1 to n do hit[a[j]+i]:=1; od: od:
[seq(a[n],n=1..M)]; [seq(m[n],n=1..M)];
  • Mathematica
    f[s_] := Block[{n, k},n = Length[s] + 1;k = Last[s] + n - Mod[Last[s], n];While[MemberQ[Union[Plus @@@ Tuples[s, 2]], k], k += n];Append[s, k]];Nest[f, {1}, 51] (* Ray Chandler, Sep 29 2006 *)

Extensions

More terms from N. J. A. Sloane and Chai Tian (Chao.Tian(AT)epfl.ch), Sep 19 2006
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.