A115034 -id:A115034 - cp's OEIS frontend

A115033 Alternately multiply and divide, with a(1)=2 and a(2)=3.

2, 3, 6, 2, 12, 6, 72, 12, 864, 72, 62208, 864, 53747712, 62208, 3343537668096, 53747712, 179707499645975396352, 3343537668096, 600858794305667322270155425185792, 179707499645975396352, 107978831564966913814384922944738457859243070439030784, 600858794305667322270155425185792

Offset: 1

Giovanni Teofilatto, Feb 26 2006

Cf. A115034, A174348.

addmul:=proc(k,m,maxn) local f:
  f:= proc(n) if n::even
    then k^combinat:-fibonacci(n/2-1)  *m^combinat:-fibonacci(n/2-2)
    else k^combinat:-fibonacci((n+1)/2)*m^combinat:-fibonacci((n-1)/2)
    fi
  end proc:
  map(f, [$1..maxn]);
end proc: # after Robert Israel in A174348
addmul(2,3,22)[]; # Georg Fischer, Jun 18 2021

nxt[{a_, b_}]:={a*b, (a*b)/b}; NestList[nxt, {2,3}, 10]//Flatten (* Georg Fischer, Jun 18 2021 *)

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

Definition adapted to offset by Georg Fischer, Jun 18 2021

Corrected and extended by Michel Marcus, May 31 2025

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

Giovanni Teofilatto, Mar 16 2010

Robert Israel, Table of n, a(n) for n = 1..32

Cf. A000045, A115033, A115034, A115043.

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

nxt[{a_,b_}]:={a*b,(a*b)/b}; NestList[nxt,{3,7},10]//Flatten (* Harvey P. Dale, Sep 06 2020 *)

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)

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

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

Giovanni Teofilatto, Feb 28 2006

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

Cf. A115033, A115034, A174348.

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).

Formulas corrected by R. J. Mathar, Mar 16 2010

cp's OEIS Frontend

A115033 Alternately multiply and divide, with a(1)=2 and a(2)=3.

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

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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).

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