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.

A166470 a(n) = 2^F(n+1)*3^F(n), where F(n) is the n-th Fibonacci number, A000045(n).

Original entry on oeis.org

2, 6, 12, 72, 864, 62208, 53747712, 3343537668096, 179707499645975396352, 600858794305667322270155425185792, 107978831564966913814384922944738457859243070439030784
Offset: 0

Views

Author

Matthew Vandermast, Nov 05 2009

Keywords

Links

Crossrefs

Subsequence of A025610 and hence of A003586 and A025487.
Cf. A000045, A000301, A002110, A010098, A115033, A166469, A174666, A230900.

Programs

  • Magma
    [2^Fibonacci(n+1)*3^Fibonacci(n): n in [0..14]]; // G. C. Greubel, Jul 29 2024
  • Mathematica
    3^First[#] 2^Last[#]&/@Partition[Fibonacci[Range[0,12]],2,1] (* Harvey P. Dale, Aug 20 2012 *)
  • PARI
    a(n)=2^fibonacci(n+1)*3^fibonacci(n) \\ Charles R Greathouse IV, Sep 19 2022
  • SageMath
    [2^fibonacci(n+1)*3^fibonacci(n) for n in range(15)] # G. C. Greubel, Jul 29 2024

Formula

a(n) = A000301(n+1)*A010098(n).
For n > 1, a(n) = a(n-1)*a(n-2).
For m > 1, n > 1, A166469(A002110(m)*(a(n)^k)/12) = k*Fibonacci(m+n).
A166469(a(n)) = Fibonacci(n+2) + 1 = A001611(n+2).
a(n) = 2 * A174666(n+1). - Alois P. Heinz, Sep 16 2022
a(n) = 2^(Fibonacci(n+1) + c*Fibonacci(n)), with c=log_2(3). Cf. A000301 (c=1) & A010098 (c=2). - Andrea Pinos, Sep 29 2022
a(n) = A115033(2*n+1). - David Radcliffe, May 31 2025

Extensions

Typo corrected by Matthew Vandermast, Nov 07 2009

A174348 Alternately multiply and divide, with a(1)=3 and a(1)=7.

Original entry on oeis.org

3, 7, 21, 3, 63, 21, 1323, 63, 83349, 1323, 110270727, 83349, 9190954824723, 110270727, 1013493270346362783621, 9190954824723, 9314970862914194811435918430261983, 1013493270346362783621
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 16 2010

Keywords

Links

Crossrefs

Cf. A000045, A115033, A115034, A115043.

Programs

  • Maple
    f:= proc(n) if n::even then 3^combinat:-fibonacci(n/2-1)*7^combinat:-fibonacci(n/2-2)
            else 3^combinat:-fibonacci((n+1)/2)*7^combinat:-fibonacci((n-1)/2)
            fi
end proc:
map(f, [$1..20]); # Robert Israel, Dec 05 2016
  • Mathematica
    nxt[{a_,b_}]:={a*b,(a*b)/b}; NestList[nxt,{3,7},10]//Flatten (* Harvey P. Dale, Sep 06 2020 *)

Formula

From Robert Israel, Dec 05 2016: (Start)
a(2k) = a(2k-3) = 3^A000045(k-1)*7^A000045(k-2) for k >=2.
a(2k+1) = a(2k)*a(2k-1) = 3^A000045(k+1)*7^A000045(k) for k>=1. (End)

Extensions

a(18) corrected by Robert Israel, Dec 05 2016

A115034 Alternately multiply and divide, with a(1)=1 and a(2)=2.

Original entry on oeis.org

1, 2, 2, 1, 2, 2, 4, 2, 8, 4, 32, 8, 256, 32, 8192, 256, 2097152, 8192, 17179869184, 2097152, 36028797018963968, 17179869184, 618970019642690137449562112, 36028797018963968
Offset: 1

Views

Author

Giovanni Teofilatto, Feb 26 2006; corrected Feb 28 2006

Keywords

Comments

a(n) = power of 2; taking the terms a(n+1)>=a(n), the sequence of exponent of power of 2 is 0,1,1,2,3,5,8,... which are the Fibonacci Numbers.

Crossrefs

Cf. A115033, A174348.

Programs

  • Mathematica
    nxt[{a_, b_}]:={a*b, (a*b)/b}; NestList[nxt, {1,2}, 10]//Flatten (* Georg Fischer, Jun 18 2021 *)

Formula

a(2*k) = a(2*k-3); a(2*k+1) = a(2*k)*a(2*k-1) - Georg Fischer, Jun 18 2021

Extensions

Definition adapted to offset by Georg Fischer, Jun 18 2021

A115043 a(0)=3, a(1)=5. a(n) = a(n-1)*a(n-2) if n odd, else a(n) = a(n-1)/a(n-2).

Original entry on oeis.org

3, 5, 15, 3, 45, 15, 675, 45, 30375, 675, 20503125, 30375, 622782421875, 20503125, 12768985843505859375, 622782421875, 7952299928506168842315673828125, 12768985843505859375
Offset: 0

Views

Author

Giovanni Teofilatto, Feb 28 2006

Keywords

Comments

All divisors >1 of the terms are also in the sequence.

Crossrefs

Cf. A115033, A115034, A174348.

Formula

a(n) = a(n-2)*a(n-4) if n odd. a(n)=a(n-3) if n even.
a(2n+1) = 3^Fibonacci(n+1) * 5^Fibonacci(n).
a(2n) = 3^Fibonacci(n-1) * 5^Fibonacci(n-2).

Extensions

Formulas corrected by R. J. Mathar, Mar 16 2010
Showing 1-4 of 4 results.

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