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 1-3 of 3 results.

A103584 Numbers in A103543 not congruent to 3 mod 4.

Original entry on oeis.org

62, 126, 190, 254, 318, 382, 446, 510, 574, 638, 702, 766, 830, 894, 958, 1021, 1022, 1086, 1150, 1214, 1278, 1342, 1406, 1470, 1534, 1598, 1662, 1726, 1790, 1854, 1918, 1982, 2045, 2046, 2110, 2174, 2238, 2302, 2366, 2430, 2494, 2558, 2622, 2686, 2750
Offset: 1

Views

Author

Benoit Cloitre and Philippe Deléham, Mar 24 2005

Keywords

Links

  • David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps], J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; Select[ Complement[ Range[2750], Select[ Range[11000], f[ # ] == 0 &]/4], Mod[ #, 4] != 3 &] (* Robert G. Wilson v, Mar 26 2005 *)

Extensions

More terms from Robert G. Wilson v, Mar 26 2005

A102370 "Sloping binary numbers": write numbers in binary under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 3, 6, 5, 4, 15, 10, 9, 8, 11, 14, 13, 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30, 61, 44, 39, 34, 33, 32, 35, 38, 37, 36, 47, 42, 41, 40, 43, 46, 45, 60, 55, 50, 49, 48, 51, 54, 53, 52, 63, 58, 57, 56, 59, 126, 93, 76, 71, 66, 65, 64, 67, 70, 69
Offset: 0

Views

Author

Philippe Deléham, Feb 13 2005

Keywords

Comments

All terms are distinct, but certain terms (see A102371) are missing. But see A103122.
Trajectory of 1 is 1, 3, 5, 15, 17, 19, 21, 31, 33, ..., see A103192.

Examples

			........0
........1
.......10
.......11
......100
......101
......110
......111
.....1000
.........
The upward-sloping diagonals are:
0
11
110
101
100
1111
1010
.......
giving 0, 3, 6, 5, 4, 15, 10, ...
The sequence has a natural decomposition into blocks (see the paper): 0; 3; 6, 5, 4; 15, 10, 9, 8, 11, 14, 13; 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30; 61, ...
Reading the array of binary numbers along diagonals with slope 1 gives this sequence, slope 2 gives A105085, slope 0 gives A001477 and slope -1 gives A105033.

Links

Crossrefs

Related sequences (1): A103542 (binary version), A102371 (complement), A103185, A103528, A103529, A103530, A103318, A034797, A103543, A103581, A103582, A103583.
Related sequences (2): A103584, A103585, A103586, A103587, A103127, A103192 (trajectory of 1), A103122, A103588, A103589, A103202 (sorted), A103205 (base 10 version).
Related sequences (3): A103747 (trajectory of 2), A103621, A103745, A103615, A103842, A103863, A104234, A104235, A103813, A105023, A105024, A105025, A105026, A105027, A105028.
Related sequences (4): A105029, A105030, A105031, A105032, A105033, A105034, A105035, A105108.
Related sequences (5): A105229, A105271, A104378, A104401, A104403, A104489, A104490, A104853, A104893, A104894, A105085.

Programs

  • Haskell
    a102370 n = a102370_list !! n
a102370_list = 0 : map (a105027 . toInteger) a062289_list
-- Reinhard Zumkeller, Jul 21 2012
  • Maple
    A102370:=proc(n) local t1,l; t1:=n; for l from 1 to n do if n+l mod 2^l = 0 then t1:=t1+2^l; fi; od: t1; end;
  • Mathematica
    f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; Table[ f[n] + n, {n, 0, 71}] (* Robert G. Wilson v, Mar 21 2005 *)
  • PARI
    A102370(n)=n-1+sum(k=0,ceil(log(n+1)/log(2)),if((n+k)%2^k,0,2^k)) \\ Benoit Cloitre, Mar 20 2005
  • PARI
    {a(n) = if( n<1, 0, sum( k=0, length( binary( n)), bitand( n + k, 2^k)))} /* Michael Somos, Mar 26 2012 */
  • Python
    def a(n): return 0 if n<1 else sum([(n + k)&(2**k) for k in range(len(bin(n)[2:]) + 1)]) # Indranil Ghosh, May 03 2017

Formula

a(n) = n + Sum_{ k >= 1 such that n + k == 0 mod 2^k } 2^k. (Cf. A103185.) In particular, a(n) >= n. - N. J. A. Sloane, Mar 18 2005
a(n) = A105027(A062289(n)) for n > 0. - Reinhard Zumkeller, Jul 21 2012

Extensions

More terms from Benoit Cloitre, Mar 20 2005

A104235 Numbers n such that A102370(n) = n.

Original entry on oeis.org

0, 4, 8, 16, 20, 24, 32, 36, 40, 48, 52, 56, 64, 68, 72, 80, 84, 88, 96, 100, 104, 112, 116, 120, 128, 132, 136, 144, 148, 152, 160, 164, 168, 176, 180, 184, 192, 196, 200, 208, 212, 216, 224, 228, 232, 240, 244, 256, 260, 264, 272, 276, 280, 288, 292, 296, 304, 308, 312
Offset: 1

Views

Author

N. J. A. Sloane, Apr 02 2005

Keywords

Comments

See A103543 and A103584 for much more about this sequence.
Indices of the 0 values in A103863.

Links

Crossrefs

Cf. A102370, A103543, A103584. Dividing by 4 gives A104401.
Cf. A105271, A214414.

Programs

  • Haskell
    a104235 n = a104235_list !! (n-1)
a104235_list = [x | x <- [0..], a102370 x == toInteger x]
-- Reinhard Zumkeller, Jul 21 2012
Showing 1-3 of 3 results.

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

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