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 1-7 of 7 results.

A081965 Diagonal of A081964.

Original entry on oeis.org

1, 5, 7, 15, 16, 31, 27, 45, 49, 73, 62, 103, 86, 129, 133, 163, 146, 217, 178, 251, 248, 293, 262, 359, 316, 399, 386, 461, 418, 569, 472, 585, 580, 657, 634, 761, 675, 813, 796, 911, 830, 1039, 908, 1083, 1072, 1171, 1088, 1313, 1192, 1399, 1334, 1489
Offset: 1

Views

Author

Amarnath Murthy, Apr 03 2003

Keywords

Crossrefs

Cf. A081964, A081966.

Formula

a(n)=A077161(n), n>2. [From R. J. Mathar, Dec 15 2008]

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 08 2003

A081966 Row sums of A081964.

Original entry on oeis.org

1, 8, 13, 48, 56, 144, 147, 294, 358, 624, 548, 1020, 978, 1576, 1685, 2340, 2048, 3456, 3036, 4454, 4481, 5870, 5188, 7722, 7289, 9560, 9365, 11976, 10889, 15378, 13729, 17066, 17330, 21168, 20051, 25428, 22997, 29048, 28817, 34428, 31444
Offset: 1

Views

Author

Amarnath Murthy, Apr 03 2003

Keywords

Crossrefs

Cf. A081964, A081965.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 08 2003

A084753 Erroneous version of A081964.

Original entry on oeis.org

1, 3, 5, 2, 4, 7, 9, 11, 13, 17, 6, 8, 12, 14, 16, 19, 23, 29, 31, 37, 41
Offset: 1

Views

Author

Keywords

A095167 Triangle read by rows in which the n-th row contains n numbers noncoprime to n and not occurring in earlier rows.

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 8, 10, 12, 14, 5, 15, 20, 25, 30, 16, 18, 21, 22, 24, 26, 7, 28, 35, 42, 49, 56, 63, 32, 34, 36, 38, 40, 44, 46, 48, 27, 33, 39, 45, 51, 54, 57, 60, 66, 50, 52, 55, 58, 62, 64, 65, 68, 70, 72, 11, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 69, 74, 75, 76
Offset: 1

Views

Author

Amarnath Murthy, Jun 01 2004

Keywords

Comments

Rearrangement of natural numbers so that next n numbers are not coprime to n.

Examples

			1
2 4
3 6 9
8 10 12 14
5 15 20 25 30
16 18 21 22 24 26
7 28 35 42 49 56 63
...

Links

Crossrefs

Cf. A095168, A095169, A095170, A095171.
Cf. A081964 (coprime instead of non-coprime).

Programs

  • Mathematica
    Fold[Function[{a, n}, Join[a, Select[Complement[Range[Max[a] + n^2], a], GCD[n, #] > 1 &, n]]], {1}, Range[2, 12]] (* Ivan Neretin, Jun 05 2015 *)
  • PARI
    S=Set();for(n=2,20,k=0;m=1;while(k1,S=setunion(S,[m]);print1(" ",m);k++))) (Alekseyev)

Extensions

More terms from Max Alekseyev, Jun 30 2005

A077159 Triangle in which n-th row contains smallest n numbers coprime to n which have not occurred earlier, with a(1)=2.

Original entry on oeis.org

2, 1, 3, 4, 5, 7, 9, 11, 13, 15, 6, 8, 12, 14, 16, 17, 19, 23, 25, 29, 31, 10, 18, 20, 22, 24, 26, 27, 21, 33, 35, 37, 39, 41, 43, 45, 28, 32, 34, 38, 40, 44, 46, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 30, 36, 42, 48, 50, 52, 54, 56, 58, 60, 62, 55, 65, 77, 79, 83, 85
Offset: 1

Views

Author

Amarnath Murthy, Oct 31 2002

Keywords

Comments

A permutation of the natural numbers.
A081964 is a better version of this sequence. - Sean A. Irvine, May 08 2025

Examples

			Triangle begins:
2
1 3
4 5 7
9 11 13 15
6 8 12 14 16
17 19 23 25 29 31
10 18 20 22 23 24 26
...

Crossrefs

Cf. A077160, A077161, A077162, A081964.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003

A090980 From the set of numbers > 1, go on deleting n smallest numbers relatively prime to n that were not deleted earlier; a(n) = the largest number deleted.

Original entry on oeis.org

2, 5, 8, 15, 17, 35, 27, 47, 50, 73, 64, 103, 87, 131, 134, 163, 148, 217, 180, 251, 248, 293, 264, 359, 318, 399, 386, 461, 420, 569, 474, 585, 580, 657, 636, 761, 676, 813, 796, 911, 832, 1039, 910, 1083, 1072, 1171, 1090, 1313, 1194, 1399, 1334, 1489, 1384
Offset: 1

Views

Author

Amarnath Murthy, Jan 23 2004

Keywords

Crossrefs

Cf. A090979.
Cf. A081964.

Extensions

More terms from David Wasserman, Feb 23 2006

A125060 Irregular array where a(1)=1; run n of the sequence is the first a(n-1) integers from among those positive integers which are coprime to n and which do not occur earlier in the sequence {a(k)}.

Original entry on oeis.org

1, 3, 2, 4, 5, 7, 9, 6, 8, 11, 12, 13, 17, 19, 23, 25, 10, 15, 16, 18, 20, 22, 24, 21, 27, 29, 31, 33, 35, 37, 39, 41, 14, 26, 28, 32, 34, 38, 43, 47, 49, 51, 53, 57, 59, 61, 30, 36, 40, 42, 45, 46, 48, 50, 52, 54, 56, 55, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 44, 58, 60
Offset: 1

Views

Author

Leroy Quet, Jan 08 2007

Keywords

Comments

This sequence is a permutation of the positive integers.

Examples

			The sequence grouped by runs, where run n, after the first 1, consists of a(n-1) terms:
1,(3),(2,4,5),(7,9),(6,8,11,12),(13,17,19,23,25),(10,15,16,18,20,22,24),...
a(5) is 5. So run 6 contains the first 5 positive integers which do not occur earlier in the sequence and which are coprime to 6, (13,17,19,23,25).

Crossrefs

Cf. A081964.

Programs

  • Mathematica
    f[l_List] := Block[{n = Length[l] + 1, fl = Flatten[l], c, k = 0, r = {}},c = fl[[n - 1]];While[c > 0,k++;While[MemberQ[fl, k] || GCD[k, n] > 1, k++ ];AppendTo[r, k];c--;];Append[l, r]];Nest[f, {{1}}, 12] // Flatten (* Ray Chandler, Feb 13 2007 *)

Extensions

Extended by Ray Chandler, Feb 13 2007
Showing 1-7 of 7 results.

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

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