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.

A120518 a(n) = min{j : A120507(j) = n}.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 86, 87, 88, 89, 91, 92
Offset: 1

Views

Author

Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006

Keywords

Links

Crossrefs

Cf. A120507, A120529.

Programs

  • Maple
    A120518 := proc(n)
    for j from 1 do
        if A120507(j) = n then
            return j ;
        end if;
    end do:
end proc:
seq(A120518(n),n=1..70) ;

Formula

G.f.: z / (1-z) * (1 + sum(z^(m^4) * (1 / (1 - z^(m^4))), m=0..infinity)).
a(1) = 1; a(n) = n-1 + a(floor((n-1)/4)+1). - Gleb Ivanov, Jan 12 2022

A120529 First differences of successive generalized meta-Fibonacci numbers A120507.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1
Offset: 1

Views

Author

Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006

Keywords

Links

Crossrefs

Cf. A120507, A120518.

Programs

Formula

d(n) = 0 if node n is an inner node, or 1 if node n is a leaf.
g.f.: z (1 + z^1 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^4 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^16 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.
g.f.: D(z) = z * prod((1 - z^(4 * [i])) / (1 - z^[i])), i=1..infinity), where [i] = (4^i - 1) / 3.

A228297 Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5.

Original entry on oeis.org

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

Views

Author

Michel Marcus, Aug 20 2013

Keywords

Comments

Each integer n appears x+1 times where x is the greatest power of 5 in the factorization of n!. - Gerald Hillier, Feb 08 2020

Links

Crossrefs

Cf. A120503, A120507, A228298.

Programs

  • Mathematica
    Array[ConstantArray[#, IntegerExponent[#, 5] + 1] &, 53] // Flatten (* Michael De Vlieger, Feb 08 2020 *)
  • PARI
    a(n)= {local(A); if(n<=5, max(0, n), A=vector(n, i, i); for(k=6, n, A[k]= A[k-A[k-1]] + A[k-1-A[k-2]] + A[k-2-A[k-3]] + A[k-3-A[k-4]] + A[k-4-A[k-5]];); A[n];);}
(HP 49G calculator)
« DUPDUP 5 IQUOT -
  WHILE DUP 0 OVER
    DO 5 IQUOT DUP
ROT + SWAP DUP NOT
    UNTIL
    END DROP +
PICK3 <
  REPEAT 1 +
  END NIP
» Gerald Hillier, Sep 19 2017

Formula

a(n) = A007845(n)/5. - M. F. Hasler, Dec 27 2019

A228298 Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=7.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 48, 49, 49, 49, 50, 51, 52, 53, 54, 55, 56, 56
Offset: 1

Views

Author

Michel Marcus, Aug 20 2013

Keywords

Comments

It appears than a(n) = A020646(n)/7 for n>0 (verified up to n=700).

Links

Crossrefs

Cf. A120503, A120507, A228297.

Programs

  • PARI
    a(n)= {local(A); if(n<=7, max(0, n), A=vector(n, i, i); for(k=8, n, A[k]= A[k-A[k-1]] + A[k-1-A[k-2]] + A[k-2-A[k-3]] + A[k-3-A[k-4]] + A[k-4-A[k-5]] + A[k-5-A[k-6]] + A[k-6-A[k-7]];); A[n];);}
Showing 1-4 of 4 results.

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