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.

A033555 Duplicate of A130134.

Original entry on oeis.org

2, 4, 8, 248, 17608, 90148, 106978, 253828, 364808
Offset: 1

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Keywords

A015922 Numbers k such that 2^k == 8 (mod k).

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219, 237, 248, 249, 267, 291, 303, 309, 315, 321, 327, 339, 381, 393, 399, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633
Offset: 1

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Keywords

Comments

For all m, 2^A015921(m) - 1 belongs to this sequence.

Crossrefs

Contains A033553 as a subsequence.
The odd terms form A276967.

Programs

  • Mathematica
    a015922Q[n_Integer] := If[Mod[2^n, n] == Mod[8, n], True, False];
    a015922[n_Integer] :=
    Flatten[Position[Thread[a015922Q[Range[n]]], True]];
    a015922[1000000] (* Michael De Vlieger, Jul 16 2014 *)
    m = 8; Join[Select[Range[m], Divisible[2^# - m, #] &], Select[Range[m + 1, 10^3], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 12 2018 *)
    Join[{1,2,3,4,8},Select[Range[650],PowerMod[2,#,#]==8&]] (* Harvey P. Dale, Aug 22 2020 *)
  • PARI
    isok(n) = Mod(2, n)^n == Mod(8, n); \\ Michel Marcus, Oct 13 2013, Jul 16 2014

Extensions

First 5 terms inserted by David W. Wilson

A130133 Terms in A015922 not divisible by 3.

Original entry on oeis.org

1, 2, 4, 8, 248, 731, 1333, 3503, 17608, 35003, 50963, 62611, 82603, 90148, 94643, 106978, 201295, 231311, 253828, 335723, 364808, 374573, 425323, 490915, 592595, 628015, 725203, 984343, 1031803, 1112023, 1136195, 1376903, 1411343, 1430003, 1642798, 1926088
Offset: 1

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Author

Zak Seidov, May 12 2007

Keywords

Comments

Intersection of A015922 and A001651. - Michel Marcus, Oct 13 2013

Crossrefs

Intersection with A033553 gives A277344.

Programs

  • Maple
    a:= proc(n) option remember; local k;
          for k from 1+`if`(n=1, 0, a(n-1)) while
          irem(k, 3)=0 or 2&^k mod k <> 8 mod k do od; k
        end:
    seq(a(n), n=1..30);  # Alois P. Heinz, Jun 04 2014
  • Mathematica
    {1, 2, 4, 8} ~Join~ Select[Range[2 10^6], PowerMod[2, #, #] == 8 && !Divisible[#, 3]&] (* Jean-François Alcover, Nov 02 2020 *)
  • PARI
    isok(n) = (n % 3) && (Mod(2^n, n) == Mod(8, n)); \\ Michel Marcus, Oct 13 2013

Extensions

a(17)-a(28) from Michel Marcus, Oct 13 2013
a(29)-a(36) from Alois P. Heinz, Jun 04 2014

A122711 Even numbers n such that n+2 divides n+2^n.

Original entry on oeis.org

106976, 1642796, 21879936, 96593696, 6926872352, 21235295216, 24936246176, 25867010016, 80832867116, 82230049056, 208329074876, 360598467776, 533800559216, 587627376176, 661575990912, 662312961696, 664490433776, 737374205276, 831623487276, 1052816473676, 1137732817376, 1213045642656, 1270015920636
Offset: 1

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Author

Zak Seidov, Sep 23 2006

Keywords

Comments

Same as even numbers n such that 2^n == 2 (mod n+2). - Robert G. Wilson v, Sep 27 2006
n must be a multiple of 4. A002326(n/4) must not be divisible by 2 or 3. If p is an odd prime factor of n+2, (n+2)/p mod A002326((p-1)/2)=3. - Martin Fuller, Oct 09 2006
Also, the positive numbers A015922(k)-2 that are multiples of 4. E.g., a(1) = 106976 = A015922(3926)-2. Hence, a(n)+2 forms a subsequence of A015922 (and of A130134) consisting of the terms congruent to 2 modulo 4. - Max Alekseyev, Apr 03 2014

Crossrefs

Programs

  • Mathematica
    Do[ If[ PowerMod[2, 2n, 2n + 2] == 2, Print@2n], {n, 10^9}] (* Robert G. Wilson v, Sep 27 2006 *)

Extensions

More terms from Max Alekseyev, Sep 23 2006, Oct 01 2006
More terms from Martin Fuller, Oct 09 2006
Terms a(18) onward from Max Alekseyev, Apr 09 2014
b-file corrected by Max Alekseyev, Oct 11 2016
Showing 1-4 of 4 results.