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 1-10 of 40 results. Next

A059127 A hierarchical sequence (W2{3} - see A059126).

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 4, 5, 4, 6, 4, 5, 4, 1, 2, 1, 3, 1, 2, 1, 7, 8, 7, 9, 7, 8, 7, 1, 2, 1, 3, 1, 2, 1, 4, 5, 4, 6, 4, 5, 4, 1, 2, 1, 3, 1, 2, 1, 10, 11, 10, 12, 10, 11, 10, 1, 2, 1, 3, 1, 2, 1, 4, 5, 4, 6, 4, 5, 4, 1, 2, 1, 3, 1, 2, 1, 7, 8, 7, 9, 7, 8, 7, 1, 2, 1, 3, 1, 2, 1, 4, 5, 4, 6, 4, 5, 4, 1, 2, 1
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Crossrefs

Cf. A001511, A059126, A059128, A059129, A059130, A059134, A059135.

Programs

  • Mathematica
    Block[{m = 3, i = 7, a}, a = IntegerExponent[2 Range@ i, 2]; Array[IntegerExponent[2 #, 2] /. k_ :> (a + m k - m) &, 15]] // Flatten (* Michael De Vlieger, Nov 02 2018 *)

Formula

a(7n+3) = 3*A001511(1+n), a(7n) = a(7n+2) = a(7n+4) = a(7n+6) = a(7n+3)-2, a(7n+1) = a(7n+5) = a(7n+3)-1. - Antti Karttunen, May 28 2017

A059134 A hierarchical sequence (W2{3}c - see A059126).

Original entry on oeis.org

11, 32, 11, 53, 11, 32, 11, 74, 11, 32, 11, 53, 11, 32, 11, 95, 11, 32, 11, 53, 11, 32, 11, 74, 11, 32, 11, 53, 11, 32, 11, 116, 11, 32, 11, 53, 11, 32, 11, 74, 11, 32, 11, 53, 11, 32, 11, 95, 11, 32, 11, 53, 11, 32, 11, 74, 11, 32, 11, 53, 11, 32, 11, 137, 11, 32, 11, 53, 11
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Crossrefs

Cf. A059126, A059127.
Cf. A059141 (7*p+11), A059144 (9*p+15), A220466. - Johannes W. Meijer, Jan 21 2013

Programs

  • Maple
    nmax:=68: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 0 to ceil(nmax/(p+2))+1 do a((2*n+1)*2^p-1) := 21*p+11 od: od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Jan 21 2013

Formula

a((2*n+1)*2^p-1) = 21*p+11 for p >= 0. - Johannes W. Meijer, Jan 21 2013
a(n) = Sum_{k=0..6} A059127(7*n+k). - Sean A. Irvine, Sep 12 2022

A059151 A hierarchical sequence (W'3{2,2}* - see A059126).

Original entry on oeis.org

1, 2, 1, 2, 4, 2, 1, 2, 1, 2, 4, 2, 4, 8, 4, 2, 4, 2, 1, 2, 1, 2, 4, 2, 1, 2, 1, 4, 8, 4, 8, 16, 8, 4, 8, 4, 1, 2, 1, 2, 4, 2, 1, 2, 1, 2, 4, 2, 4, 8, 4, 2, 4, 2, 1, 2, 1, 2, 4, 2, 1, 2, 1, 8, 16, 8, 16, 32, 16, 8, 16, 8, 1, 2, 1, 2, 4, 2, 1, 2, 1, 2, 4, 2, 4, 8, 4, 2, 4, 2, 1, 2, 1, 2, 4, 2, 1, 2, 1, 4
Offset: 0

Views

Author

Jonas Wallgren, Feb 01 2001

Keywords

Links

A059128 A hierarchical sequence (W3{2,2} - see A059126).

Original entry on oeis.org

1, 2, 1, 3, 4, 3, 1, 2, 1, 5, 6, 5, 7, 8, 7, 5, 6, 5, 1, 2, 1, 3, 4, 3, 1, 2, 1, 9, 10, 9, 11, 12, 11, 9, 10, 9, 1, 2, 1, 3, 4, 3, 1, 2, 1, 5, 6, 5, 7, 8, 7, 5, 6, 5, 1, 2, 1, 3, 4, 3, 1, 2, 1, 13, 14, 13, 15, 16, 15, 13, 14, 13, 1, 2, 1, 3, 4, 3, 1, 2, 1, 5, 6, 5, 7, 8, 7, 5, 6, 5, 1, 2, 1, 3, 4, 3, 1, 2
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Formula

a(3n+1) = 2*A059126(1+n), a(3n) = a(3n+2) = a(3n+1) - 1. - Sean A. Irvine, Sep 12 2022

A059129 A hierarchical sequence (W2{2}* - see A059126).

Original entry on oeis.org

1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 5, 6, 5, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 6, 7, 6, 1, 2, 1, 2, 3, 2, 1, 2, 1
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Comments

Begin with the empty finite sequence s_0. Inductively extend s_n to obtain s_{n+1} as follows: if s_n is given by a, b, c, ..., d, e, f, with g being the least integer that is not a value of s_n, then s_{n+1} is a, b, c, ..., d, e, f, g, -f, -e, -d, ..., -c, -d, -a, -g. The terms of {a(n)} give the absolute values of the limit of these sequences. These finite sequences naturally describe elements of fundamental groups occurring in picture-hanging puzzles and Brunnian links. - Thomas Anton, Oct 15 2022

Links

Crossrefs

Cf. A034947, A059126.

A059132 A hierarchical sequence (W2{2}c - see A059126).

Original entry on oeis.org

4, 10, 4, 16, 4, 10, 4, 22, 4, 10, 4, 16, 4, 10, 4, 28, 4, 10, 4, 16, 4, 10, 4, 22, 4, 10, 4, 16, 4, 10, 4, 34, 4, 10, 4, 16, 4, 10, 4, 22, 4, 10, 4, 16, 4, 10, 4, 28, 4, 10, 4, 16, 4, 10, 4, 22, 4, 10, 4, 16, 4, 10, 4, 40, 4, 10, 4, 16, 4, 10, 4, 22, 4, 10, 4, 16, 4, 10, 4, 28, 4, 10, 4, 16
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Crossrefs

Cf. A007814, A059126, A059134, A059137, A059139.

Programs

Formula

a(n) = 4 + 6*A007814(n+1). a(2n) = 4, a(2n+1) = a(n) + 6. - Ralf Stephan, Oct 09 2003. Typo in the first formula corrected by Antti Karttunen, Nov 01 2018
a(n) = A059126(3*n) + A059126(3*n+1) + A059126(3*n+2). - Sean A. Irvine, Sep 12 2022

A059144 A hierarchical sequence (W3{2,2}*cc - see A059126).

Original entry on oeis.org

15, 24, 15, 33, 15, 24, 15, 42, 15, 24, 15, 33, 15, 24, 15, 51, 15, 24, 15, 33, 15, 24, 15, 42, 15, 24, 15, 33, 15, 24, 15, 60, 15, 24, 15, 33, 15, 24, 15, 42, 15, 24, 15, 33, 15, 24, 15, 51, 15, 24, 15, 33, 15, 24, 15, 42, 15, 24, 15, 33, 15, 24, 15, 69, 15, 24, 15, 33, 15
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Crossrefs

Cf. A059126, A059143.

Formula

a(n) = A059143(3*n) + A059143(3*n+1) + A059143(3*n+2). - Sean A. Irvine, Sep 13 2022

A059133 A hierarchical sequence (S(W2{2}c) - see A059126).

Original entry on oeis.org

4, 18, 52, 126, 280, 594, 1228, 2502, 5056, 10170, 20404, 40878, 81832, 163746, 327580, 655254, 1310608, 2621322, 5242756, 10485630, 20971384, 41942898, 83885932, 167772006, 335544160, 671088474, 1342177108, 2684354382, 5368708936, 10737418050, 21474836284, 42949672758, 85899345712
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Formula

Conjectures from Colin Barker, Oct 07 2015: (Start)
a(n) = 4*(-4+5*2^n)-6*n.
a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3) for n>2.
G.f.: -2*(x+2) / ((x-1)^2*(2*x-1)).
(End)
From Charlie Neder, Sep 15 2018: (Start)
a(1) is the sum of the first phrase, (1,2,1).
W2{2}c can be generated by starting with (1,2,1) as W(1) and repeatedly applying W(n) = W(n-1) + (2n-1,2n,2n-1) + W(n-1), which implies a(n) = 2*a(n-1) + 6n - 2, from which the formulas follow. (End)
a(n) = 2*A213387(n+2). - R. J. Mathar, Apr 13 2019

Extensions

More terms via the rational g.f. - R. J. Mathar, Apr 13 2019

A059137 A hierarchical sequence (W3{2,2}cc - see A059126).

Original entry on oeis.org

18, 54, 18, 90, 18, 54, 18, 126, 18, 54, 18, 90, 18, 54, 18, 162, 18, 54, 18, 90, 18, 54, 18, 126, 18, 54, 18, 90, 18, 54, 18, 198, 18, 54, 18, 90, 18, 54, 18, 126, 18, 54, 18, 90, 18, 54, 18, 162, 18, 54, 18, 90, 18, 54, 18, 126, 18, 54, 18, 90, 18, 54, 18, 234, 18, 54
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Crossrefs

Cf. A037227, A059126, A059136.

Formula

a(n) = 18*A037227(n). - Mitch Harris, Jun 29 2005
a(n) = A059136(3*n) + A059136(3*n+1) + A059136(3*n+2). - Sean A. Irvine, Sep 13 2022

A059141 A hierarchical sequence (W2{3}*c - see A059126).

Original entry on oeis.org

11, 18, 11, 25, 11, 18, 11, 32, 11, 18, 11, 25, 11, 18, 11, 39, 11, 18, 11, 25, 11, 18, 11, 32, 11, 18, 11, 25, 11, 18, 11, 46, 11, 18, 11, 25, 11, 18, 11, 32, 11, 18, 11, 25, 11, 18, 11, 39, 11, 18, 11, 25, 11, 18, 11, 32, 11, 18, 11, 25, 11, 18, 11, 53, 11, 18, 11, 25, 11
Offset: 0

Views

Author

Jonas Wallgren, Jan 19 2001

Keywords

Links

Showing 1-10 of 40 results. Next

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