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.

A200063 Indices n where A079878(n) = n.

Original entry on oeis.org

1, 2, 8, 32, 46, 392, 12230, 155942, 659488, 1025582, 1047128, 3437088, 1449322158, 1452777560, 1691887144, 4558298126, 4840156480, 39554086678, 353617531486, 608231808384, 619986226720, 969355365422
Offset: 1

Views

Author

R. J. Mathar, Nov 13 2011

Keywords

Comments

a(23) > 4*10^12. - Donovan Johnson, Nov 21 2011

Examples

			A079878(46)=46, which adds 46 to the sequence.

Crossrefs

Cf. A200064

Programs

  • Haskell
    import Data.List (elemIndices)
a200063 n = a200063_list !! (n-1)
a200063_list = map (+ 1) $ elemIndices 0 $ zipWith (-) [1..] a079878_list
-- Reinhard Zumkeller, Nov 13 2011

Formula

{n: A079878(n)=n}.

Extensions

a(13)-a(22) from Donovan Johnson, Nov 21 2011

A200087 Smallest number m such that A079878(m) = n.

Original entry on oeis.org

1, 2, 53, 5, 71, 26, 9, 8, 19, 72, 149, 27, 91, 18, 21, 17, 43, 20, 29, 50, 35, 150, 45, 28, 99, 92, 773, 34, 171, 42, 33, 32, 123, 44, 49, 41, 75227, 58, 137, 51, 295, 48, 789, 68, 47, 46, 65, 57, 891, 100, 269, 90, 111, 428, 921, 64, 131, 172, 105, 203
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 13 2011

Keywords

Comments

A079878(a(n)) = n and A079878(m) <> n for m < a(n).

Links

Programs

  • Haskell
    import Data.List (elemIndex)
import Data.Maybe (fromJust)
a200087 n = (fromJust $ elemIndex n a079878_list) + 1

A064434 a(n) = (2*a(n-1) + 1) mod n.

Original entry on oeis.org

0, 1, 0, 1, 3, 1, 3, 7, 6, 3, 7, 3, 7, 1, 3, 7, 15, 13, 8, 17, 14, 7, 15, 7, 15, 5, 11, 23, 18, 7, 15, 31, 30, 27, 20, 5, 11, 23, 8, 17, 35, 29, 16, 33, 22, 45, 44, 41, 34, 19, 39, 27, 2, 5, 11, 23, 47, 37, 16, 33, 6, 13, 27, 55, 46, 27, 55, 43, 18, 37, 4, 9, 19, 39, 4, 9, 19, 39, 0
Offset: 1

Views

Author

Jonathan Ayres (JonathanAyres(AT)btinternet.com), Oct 01 2001

Keywords

Comments

a(n) is the remainder when (2*a(n-1) + 1) is divided by n.
Can be generalized to a(n) = f(a(n-1)) mod n, where f is any polynomial function.

Examples

			0, (0*2+1) mod 2 = 1, (1*2+1) mod 3 = 0, (0*2+1) mod 4 = 1, (1*2+1) mod 5 = 3 (3*2+1) mod 6 = 1.

Links

Crossrefs

Cf. A064456, A079878.

Programs

  • GAP
    a:=[0];; for n in [2..90] do a[n]:=(2*a[n-1]+1) mod n; od; a; # Muniru A Asiru, Jun 24 2018
  • Magma
    [n le 1 select n-1 else (2*Self(n-1)+1) mod n: n in [1..80]]; // Vincenzo Librandi, Jun 24 2018
  • Mathematica
    nxt[{n_,a_}]:={n+1,Mod[2a+1,n+1]}; Transpose[NestList[nxt,{1,0},80]][[2]] (* Harvey P. Dale, Feb 10 2014 *)
  • PARI
    { a=0; for (n=1, 1000, a=(2*a + 1)%n; write("b064434.txt", n, " ", a); ) } \\ Harry J. Smith, Sep 13 2009

Formula

a(n) = (a(n-1) * 2 + 1) mod n.

A064456 A064434(n) = 0.

Original entry on oeis.org

1, 3, 79, 235, 431, 1503, 2943, 6059, 6619, 18911, 54223, 302467995, 1772665631, 2148845167, 5145362667, 129465909327, 212089391807
Offset: 1

Views

Author

Jonathan Ayres (JonathanAyres(AT)btinternet.com), Oct 01 2001

Keywords

Comments

a(18) > 4*10^12. - Donovan Johnson, Jan 19 2011
Also indices n where A079878(n)=1. - R. J. Mathar, Nov 13 2011

Crossrefs

Cf. A064433.

Programs

  • ARIBAS
    : a := 0; for n := 1 to 3000000000 do am := a; a := (am*2 + 1) mod n; if a = 0 then write(n," "); end; end;

Extensions

More terms from Klaus Brockhaus, Oct 04 2001
Offset corrected and a(15)-a(17) from Donovan Johnson, Jan 19 2011
Showing 1-4 of 4 results.

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