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.

A104737 Positions of records in A104705.

Original entry on oeis.org

1, 2, 3, 5, 8, 9, 14, 17, 23, 26, 27, 32, 41, 44, 53, 54, 59, 62, 72, 77, 89, 90, 99, 104, 113, 116, 117, 134, 135, 143, 152, 161, 171, 176, 179, 189, 194, 206, 212, 224, 225, 233, 251, 252, 261, 266, 270, 284, 302, 314, 323, 324, 329, 332, 342, 347, 360
Offset: 1

Views

Author

Zak Seidov, Mar 21 2005

Keywords

Crossrefs

Cf. A104705, A104738, A104739.

Extensions

Extended by Ray Chandler, Jan 19 2012

A104706 First terms in the rearrangements of integer numbers (see comments).

Original entry on oeis.org

1, 2, 3, 1, 4, 5, 1, 2, 6, 1, 7, 3, 1, 2, 8, 1, 9, 4, 1, 2, 10, 1, 3, 11, 1, 2, 5, 1, 12, 13, 1, 2, 3, 1, 4, 6, 1, 2, 14, 1, 15, 3, 1, 2, 7, 1, 5, 4, 1, 2, 16, 1, 3, 17, 1, 2, 8, 1, 18, 6, 1, 2, 3, 1, 4, 19, 1, 2, 5, 1, 9, 3, 1, 2, 20, 1, 21, 4, 1, 2, 7, 1, 3, 10, 1, 2, 22, 1, 5, 6, 1, 2, 3, 1, 4, 23, 1
Offset: 1

Views

Author

Zak Seidov, Mar 19 2005

Keywords

Comments

Take the sequence of natural numbers:
s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
Move the first term s(1)=1 to 2*1 places to the right:
s1=2,3,1,4,5,6,7,8,9,10,11,12,13,14,15,16,
Move the first term s(1)=2 to 2*2 places to the right:
s2=3,1,4,5,2,6,7,8,9,10,11,12,13,14,15,16,
Repeating the procedure we get successively:
s3=1,4,5,2,6,7,3,8,9,10,11,12,13,14,15,16,
s4=4,5,1,2,6,7,3,8,9,10,11,12,13,14,15,16,
s5=5,1,2,6,7,3,8,9,4,10,11,12,13,14,15,16,
s6=1,2,6,7,3,8,9,4,10,11,5,12,13,14,15,16,
.......................................................................
s100=8,3,1,2,24,25,4,5,12,7,6,26,9,27,13,28,29,10,14,30,31,15,11,
32,33,16,34,35,17,36,37,18,38,39,19,40,41,20,42,43,21,44,45,22,
46,47,23,48,49,50,51,52,53,54,55,56,57,58,59,60,
The sequence A104706 gives the first terms in the rearrangements s0,s1,s2,...,s100. Cf. A104705

Links

Crossrefs

Cf. A104705, A028920.

Programs

  • Maple
    A104706:= proc(N) # to produce a(1) .. a(N)
    local A, R, n,M;
    M:= N;
    R:= $1..M;
    A[1]:= 1;
    for n from 2 to N do
       if 2*R[1]+1 > M then
         R:= R, [$M+1..M+N]
       fi;
       R:= R[2..2*R[1]+1],R[1],R[2*R[1]+2..N];
       A[n]:= R[1];
    od:
    seq(A[n], n=1..N);
end proc:
A104706(100); # Robert Israel, Dec 04 2015
  • Mathematica
    s=Range[100];bb={1};Do[s=Drop[Insert[s, s[[1]], 2+2s[[1]]], 1];bb=Append[bb, s[[1]]], {i, 100}];bb
NestList[Rest[Insert[#, #[[1]], 2 + 2 #[[1]]]] &, Range[30], 30][[All, 1]] (* Birkas Gyorgy, Mar 03 2011 *)
  • Sage
    def A104706(n):
    m, N = 2, 2*n-1
    while true:
        if m.divides(N): return m-2
        N = N*(m-1)//m
        m += 1
print([A104706(n) for n in (1..97)]) # Peter Luschny, Dec 04 2015

Formula

a(n) = A028920(2n-1)-1. - Benoit Cloitre, Mar 09 2007

A104717 First terms in the rearrangements of integer numbers (see comments).

Original entry on oeis.org

1, 2, 3, 4, 1, 5, 6, 7, 1, 2, 8, 9, 1, 10, 3, 11, 1, 2, 12, 13, 1, 4, 14, 15, 1, 2, 16, 3, 1, 5, 17, 18, 1, 2, 19, 6, 1, 20, 4, 3, 1, 2, 21, 22, 1, 7, 23, 24, 1, 2, 25, 5, 1, 3, 8, 26, 1, 2, 4, 27, 1, 28, 9, 29, 1, 2, 3, 6, 1, 30, 31, 10, 1, 2, 32, 4, 1, 5, 3, 33, 1, 2, 34, 7, 1, 11, 35, 36, 1, 2
Offset: 1

Views

Author

Zak Seidov, Mar 20 2005

Keywords

Comments

Take the sequence of natural numbers:
s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
Move the first term s(1)=1 to 3*1=3 places to the right:
s1=2,3,4,1,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
Move the first term s(1)=2 to 3*2=6 places to the right:
s2={3,4,1,5,6,7,2,8,9,10,11,12,13,14,15,16,17,18,19,20,
Repeating the procedure we get successively:
s3={4,1,5,6,7,2,8,9,10,3,11,12,13,14,15,16,17,18,19,20,
s4={1,5,6,7,2,8,9,10,3,11,12,13,4,14,15,16,17,18,19,20,
s5={5,6,7,1,2,8,9,10,3,11,12,13,4,14,15,16,17,18,19,20,
s6={6,7,1,2,8,9,10,3,11,12,13,4,14,15,16,5,17,18,19,20,
s7={7,1,2,8,9,10,3,11,12,13,4,14,15,16,5,17,18,19,6,20,
........................................................................
s100=1,5,39,3,2,40,13,41,42,4,43,9,14,7,44,45,46,6,15,47,10,48,49,16,8,50,
51,52,11,17,53,54,55,18,56,12,57,58,19,59,60,61,20,62,63,64,21,65,66,67,22,
68,69,70,23,71,72,73,24,74,75,76,25,77,78,79,26,80,81,82,27,83,84,85,28,86,
87,88,29,89,90,91,30,92,93,94,31,95,96,97,32,98,99,100,33,101,102,103,34,
104,105,106,35,107,108,109,36,110,111,112,37,113,114,115,38,116,117,
The sequence A104717 gives the first terms in the rearrangements s0,s1,s2,...,s100. Cf. A104705, A104706

Crossrefs

Cf. A104705, A104706.

Programs

  • Mathematica
    s=Range[200];bb={1};Do[s=Drop[Insert[s, s[[1]], 2+3 s[[1]]], 1];bb=Append[bb, s[[1]]], {i, 100}];bb

A104741 First terms in the rearrangements of integer numbers (see comments).

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 4, 5, 3, 2, 1, 6, 7, 4, 8, 9, 10, 11, 5, 3, 2, 1, 12, 13, 6, 14, 15, 16, 17, 7, 4, 18, 19, 8, 20, 21, 22, 23, 9, 24, 25, 26, 27, 28, 29, 10, 30, 31, 11, 5, 3, 2, 1, 32, 33, 34, 35, 36, 37, 12, 38, 39, 40, 41, 13, 6, 42, 43, 14, 44, 45, 46, 47, 15, 48, 49, 50, 51, 52, 53
Offset: 1

Views

Author

Zak Seidov, Mar 21 2005

Keywords

Comments

Take the sequence of natural numbers: s0=1,2,3,4,5,6,7,8,9,10,11, Repeating the procedure: "Move the first term s(1) after s(1)-th prime": we get successively: s1=2,1,3,4,5,6,7,8,9,10,11, s2=1,3,2,4,5,6,7,8,9,10,11, s3=3,2,1,4,5,6,7,8,9,10,11, s4=2,1,4,5,3,6,7,8,9,10,11, s5=1,4,5,3,2,6,7,8,9,10,11, ............................................................ s100=8,68,69,70,71,20,72,73,21,74,75,76,77,78,79,22,80,81,82, 83,23,9,84,85,86,87,88,89,24,90,91,92,93,94,95,96,97,25,98,99, 100,101,26,102,103,27,104,105,106,107,28,108,109,29,10,110, The sequence A104741 gives the first terms in the rearrangements s0,s1,s2,... Cf. A104705, A104706, A104717

Crossrefs

Cf. A104705, A104706, A104717.
Showing 1-4 of 4 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.