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.

A087824 a(n) = number of times n occurs in A087817.

Original entry on oeis.org

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

Views

Author

Roger L. Bagula, Oct 06 2003

Keywords

Crossrefs

Cf. A087817.

Programs

  • Mathematica
    Conway[n_Integer?Positive] := Conway[n] =Conway[Conway[Conway[n-1]]] + Conway[n - Conway[n-1]]
Conway[1] = Conway[2] = 1
a=Table[Conway[n], {n, 1, 3000}];
mx=Max[a]
c=Table[Count[a, m-1, m], {m, 1, mx}]
d=Delete[c, 1]

A087836 a(n) = a(a(a(a(n-1)))) + a(n - a(n-1)) with a(1)=a(2)=1.

Original entry on oeis.org

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

Views

Author

Roger L. Bagula, Oct 07 2003

Keywords

Links

Crossrefs

Cf. A004001. Different from A087817.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<3, 1,
      a(a(a(a(n-1)))) +a(n-a(n-1)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 06 2017
  • Mathematica
    a[n_Integer?Positive] := a[n] =a[a[a[a[n-1]]]] + a[n - a[n-1]]; a[1] = a[2] = 1; Table[a[n], {n, 1, 256}]
  • PARI
    lista(nn) = {va = vector(nn); va[1] = 1; va[2] = 1; for (n=3, nn, va[n] = va[va[va[va[n-1]]]]+va[n-va[n-1]];); va;} \\ Michel Marcus, Aug 06 2017

Extensions

Corrected by Michel Marcus, Aug 06 2017

A091497 Number of nonzero terms in the n-th row of triangle A091492.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21
Offset: 0

Views

Author

Paul D. Hanna, Jan 16 2004

Keywords

Crossrefs

Cf. A091492, A091493. Different from A087817 and A087836.

A107436 a(n) = (a^5)(n-1) + a(n-a(n-1)) = a(a(a(a(a(n-1))))) + a(n-a(n-1)), a(1) = a(2) = 1.

Original entry on oeis.org

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

Views

Author

Roger L. Bagula, May 26 2005

Keywords

Comments

Multi-recursive sequence suggested by A004001: 5th level.
If A004001 is a level 2 recursion, A087817 is a level 3, and A087836 is a level 4, then this sequence is the 5th level. Other multi-recursives approximate this sequence for initial terms: A087845, A087847 Benoit Cloitre's sequence is: d = Table[Ceiling[n^.56], {n, 1, digits}].
Satisfies a(n) = A002024(n-1) up to n=2280, but is strictly larger thereafter. The graph shows an interesting "phase break" (author's terms in A087836) just after 2281. Are there other such "irregularities" to be expected (when a(n) attains 2281, or later)? - M. F. Hasler, Apr 20 2014

Examples

			From n=2 to n=2280, a(n)=A002024(n-1); in particular, a(2280)=68 is preceded by 67 copies of 67. But a(2281) = a(a(a(a(a(2280))))) + a(2281-a(2280)) = a(a(a(a(68)))) + a(2281-68) = a(a(a(12))) + a(2213) = a(a(5)) + 67 =69. - _M. F. Hasler_, Apr 21 2014

Links

Crossrefs

Cf. A028310, A004001, A087817, A087836, A087845, A087847.

Programs

  • Maple
    a := proc(n) option remember; `if`(n<3,1,(a@@(5))(n-1)+a(n-a(n-1))) end; # Peter Luschny, Apr 23 2014
  • Mathematica
    a[1] = a[2] = 1; a[n_Integer?Positive] := a[n] = Nest[a, n-1, 5] + a[n - a[n - 1]]; Table[a[n], {n, 1, 255}]
  • PARI
    a107436=[1,1]; A107436(n)={if(n>#a107436, a107436=concat(a107436,vector(n-#a107436)), a107436[n] && return(a107436[n])); t=A107436(n-1); a107436[n]=A107436(n-t)+A107436(A107436(A107436(A107436(t))))} \\ M. F. Hasler, Apr 21 2014
Showing 1-4 of 4 results.

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