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 1-6 of 6 results.

A051147 Smallest m such that A051145(m) = 2^n.

Original entry on oeis.org

1, 2, 3, 5, 9, 12, 17, 29, 45, 81, 105, 177, 245, 323, 569, 893, 1277, 2121, 3221, 4853, 7697, 11015, 15333, 25841, 40157, 59213, 84239, 135107, 184679, 265277, 445029, 606509, 830411, 1394489, 1973405, 2683997, 4176989, 6710687, 9906153, 15114275, 22269021
Offset: 0

Views

Author

N. J. A. Sloane, E. M. Rains

Keywords

Crossrefs

Cf. A000079, A051145, subsequence of A244747.

Programs

  • Haskell
    import Data.List (elemIndex); import Data.Maybe (fromJust)
a051147 = fromJust . (`elemIndex` a051145_list) . (2 ^)
-- Reinhard Zumkeller, Jul 05 2014
  • Mathematica
    Block[{a, b, s}, a[0] = 0; a[1] = 1; a[n_] := a[n] = (b = 0; While[b++; BitOr[b, a[n - 1]] <= BitOr[a[n - 2], a[n - 1]]]; b); s = Array[a, 2^10, 0]; Array[FirstPosition[s, 2^#][[1]] - 1 &, Floor@ Log2@ Max@ s + 1, 0]] (* Michael De Vlieger, Aug 25 2021, after Jean-François Alcover at A051145 *)

Formula

A051145(a(n)) = 2^n. - Reinhard Zumkeller, Jul 05 2014

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000
a(21)-a(23) from Reinhard Zumkeller, Jul 05 2014
Definition corrected by Reinhard Zumkeller, Jul 05 2014
a(24)-a(30) from Charlie Neder, Oct 12 2018
More terms from Sean A. Irvine, Aug 25 2021

A244747 Positions at which powers of 2 occur in A051145.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 12, 17, 29, 45, 48, 81, 105, 108, 177, 245, 323, 324, 569, 648, 893, 1277, 1296, 2121, 2592, 3221, 4853, 5184, 7697, 11015, 15333, 15552, 25841, 31104, 40157, 59213, 84239, 93312, 135107, 184679, 265277, 279936, 445029, 606509, 830411, 839808
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 05 2014

Keywords

Comments

A209229(A051145(a(n))) = 1;
the definition of this sequence was the original definition of A051147.

Links

Crossrefs

Cf. A209229, A051147 (subsequence).

Programs

  • Haskell
    import Data.List (findIndices)
a244747 n = a244747_list !! (n-1)
a244747_list = findIndices ((== 1) . a209229) a051145_list
(C++)
See Links section.

Extensions

More terms from Rémy Sigrist, Oct 09 2022

A051146 Sequence b(n) mentioned in A051145.

Original entry on oeis.org

1, 3, 6, 7, 11, 12, 13, 15, 22, 23, 31, 56, 57, 59, 62, 63, 99, 100, 101, 103, 110, 111, 119, 120, 121, 123, 126, 127, 171, 172, 173, 175, 190, 191, 239, 240, 241, 243, 246, 247, 251, 252, 253, 255, 310, 311, 319, 328, 329, 331, 334, 335, 339, 340, 341, 343
Offset: 1

Views

Author

N. J. A. Sloane, E. M. Rains

Keywords

Links

Crossrefs

Cf. A051145.

Programs

  • Haskell
    import Data.Bits ((.|.))
a051146 n = a051146_list !! (n-1)
a051146_list = zipWith (.|.) a051145_list $ tail a051145_list
-- Reinhard Zumkeller, Oct 25 2012
  • Mathematica
    (* a5 = A051145 *) a5[0] = 0; a5[1] = 1; a5[n_] := a5[n] = (b = 0; While[b++; BitOr[b, a5[n-1]] <= BitOr[a5[n-2], a5[n-1]]]; b); a[n_] := BitOr[a5[n], a5[n+1]]; Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jan 09 2013 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000

A057923 a(0)=0, a(1)=2, a(n) = smallest number such that sequence b(n) = {a(n-1) BITWISE OR a(n)} is strictly monotonically increasing.

Original entry on oeis.org

0, 2, 1, 4, 2, 5, 8, 6, 9, 16, 10, 17, 12, 18, 13, 32, 14, 33, 16, 34, 17, 36, 18, 37, 24, 38, 25, 64, 26, 65, 28, 66, 29, 96, 30, 97, 128, 98, 129, 100, 130, 101, 136, 102, 137, 112, 138, 113, 140, 114, 141, 256, 142, 257, 144, 258, 145, 260, 146, 261, 152, 262, 153
Offset: 0

Views

Author

Larry Reeves (larryr(AT)acm.org), Oct 03 2000

Keywords

Comments

Conjecture: a(n+2) > a(n). - Robert Israel, Aug 13 2017

Examples

			See example in A051145.

Links

Crossrefs

Cf. A051145, A057924, A057925.

Programs

  • Maple
    A[0]:= 0: A[1]:= 2: B[1]:= 2:
for n from 2 to 100 do
  for k from B[n-1]-A[n-1] do
    b:= Bits:-Or(A[n-1],k);
    if b > B[n-1] then A[n]:= k; B[n]:= b; break fi
  od
od:
seq(A[i],i=0..100); # Robert Israel, Aug 13 2017

A057926 a(0) = 1, a(1) = 3, a(n) = smallest number such that sequence b(n) = a(n) OR a(n+1) is strictly monotonically increasing.

Original entry on oeis.org

1, 3, 4, 8, 5, 10, 16, 11, 20, 32, 21, 34, 24, 35, 28, 64, 29, 66, 32, 67, 36, 72, 37, 74, 48, 75, 52, 128, 53, 130, 56, 131, 60, 192, 61, 194, 256, 195, 260, 200, 261, 202, 272, 203, 276, 224, 277, 226, 280, 227, 284, 512, 285, 514, 288, 515, 292, 520, 293, 522, 304
Offset: 0

Views

Author

Larry Reeves (larryr(AT)acm.org), Oct 03 2000

Keywords

Examples

			See example in A051145.

Crossrefs

Cf. A051145, A057927, A057928.

A057929 a(0)=2, a(1)=5, a(n) = smallest number such that sequence b(n) = a(n) OR a(n+1) is strictly monotonically increasing.

Original entry on oeis.org

2, 5, 8, 6, 9, 16, 10, 17, 12, 18, 13, 32, 14, 33, 16, 34, 17, 36, 18, 37, 24, 38, 25, 64, 26, 65, 28, 66, 29, 96, 30, 97, 128, 98, 129, 100, 130, 101, 136, 102, 137, 112, 138, 113, 140, 114, 141, 256, 142, 257, 144, 258, 145, 260, 146, 261, 152, 262, 153, 288, 154
Offset: 0

Views

Author

Larry Reeves (larryr(AT)acm.org), Oct 03 2000

Keywords

Examples

			See example in A051145

Crossrefs

Cf. A051145, A057930, A057931.
Showing 1-6 of 6 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.