A145277 -id:A145277 - cp's OEIS frontend

A145275 a(n) = A145232(n+1)/A145232(n).

15005, 792070839820228500005, 311759807762174781605301007201736860141952393239819056256447450170889021063181630442743411596527196875005

Offset: 1

Artur Jasinski, Oct 06 2008

nonn

A member of the family of sequences of type:
(G^(k^(n + 1)) - (1 - G)^(k^(n + 1)))/(G^(k^n) - (1 - G)^(k^n)) where G = (1 + sqrt(5))/2.
For k=2 see A001566.
For k=3 see A002814(n+2).
For k=4 see A145274.
For k=5 see this sequence.
For k=6 see A145276.
For k=7 see A145277.

Amiram Eldar, Table of n, a(n) for n = 1..4

Cf. A001566, A001622, A002814, A145232, A145274, A145276, A145277.

G = (1 + Sqrt[5])/2; Table[Expand[(G^(5^(n + 1)) - (1 - G)^(5^(n + 1)))/Sqrt[5]]/Expand[(G^(5^n) - (1 - G)^(5^n))/Sqrt[5]], {n, 1, 5}]

a(n) = (G^(5^(n + 1)) - (1 - G)^(5^(n + 1)))/(G^(5^n) - (1 - G)^(5^n)) where G = (1 + sqrt(5))/2.

A145274 a(n) = A145231(n+1)/A145231(n).

Original entry on oeis.org

329, 10749959329, 13354478338703157414450712411084788083329

Offset: 1

Artur Jasinski, Oct 06 2008

nonn

A member of the family of sequences of type:
(G^(k^(n + 1)) - (1 - G)^(k^(n + 1)))/(G^(k^n) - (1 - G)^(k^n)) where G = (1 + sqrt(5))/2.
For k=2 see A001566.
For k=3 see A002814(n+2).
For k=4 see this sequence.
For k=5 see A145275.
For k=6 see A145276.
For k=7 see A145277.

Amiram Eldar, Table of n, a(n) for n = 1..5

Cf. A001566, A002814, A145231, A145274, A145275, A145276, A145277.

G = (1 + Sqrt[5])/2; Table[Expand[(G^(4^(n + 1)) - (1 - G)^(4^(n + 1)))/Sqrt[5]]/Expand[(G^(4^n) - (1 - G)^(4^n))/Sqrt[5]], {n, 1, 5}]

a(n) = (G^(4^(n + 1)) - (1 - G)^(4^(n + 1)))/(G^(4^n) - (1 - G)^(4^n)) where G = (1 + sqrt(5))/2.

A145276 a(n) = A145233(n+1)/A145233(n).

Original entry on oeis.org

1866294, 41473935220454958813340461622291147206

Offset: 1

Artur Jasinski, Oct 06 2008

A member of the family of sequences of type:
(G^(k^(n + 1)) - (1 - G)^(k^(n + 1)))/(G^(k^n) - (1 - G)^(k^n)) where G = (1 + sqrt(5))/2.
For k=2 see A001566.
For k=3 see A002814(n+2).
For k=4 see A145274.
For k=5 see A145275.
For k=6 see this sequence.
For k=7 see A145277.

Amiram Eldar, Table of n, a(n) for n = 1..3

Cf. A001566, A001622, A002814, A145233, A145274, A145275, A145277.

G = (1 + Sqrt[5])/2; Table[Expand[(G^(6^(n + 1)) - (1 - G)^(6^(n + 1)))/Sqrt[5]]/Expand[(G^(6^n) - (1 - G)^(6^n))/Sqrt[5]], {n, 1, 5}]

a(n) = (G^(6^(n + 1)) - (1 - G)^(6^(n + 1)))/(G^(6^n) - (1 - G)^(6^n)) where G = (1 + sqrt(5))/2.

A181419 Numbers of the form Fibonacci(p^{k+1})/Fibonacci(p^k) where p are primes, k>=1.

Original entry on oeis.org

3, 7, 17, 47, 2207, 5777, 15005, 4870847, 598364773, 192900153617, 23725150497407, 792070839820228500005, 97415813466381445596089, 562882766124611619513723647, 400009475456580321242184872389193

Offset: 1

Vladimir Shevelev, Oct 18 2010

nonn

The union of A001566 (p=2), A002814 except the first two terms (p=3), A145275 (p=5), A145277 (p=7), etc.

Robert Israel, Table of n, a(n) for n = 1..44

Cf. A001566, A002814, A145275, A145277.

N:= 10^50: # for terms <= N
S:= {}: p:= 1:
do
 p:= nextprime(p);
 v:= combinat:-fibonacci(p);
 for k from 2 do
   w:= v;
   v:= combinat:-fibonacci(p^k);
   r:= v/w;
   if r > N then break fi;
   S:= S union {r};
 od;
 if k = 2 then break fi;
od:
sort(convert(S,list)); # Robert Israel, Apr 09 2024

t = Sort@ Flatten[ Table[ {Prime[n]^(e + 1), Prime[n]^e}, {n, 8}, {e, 10}], 1]; u = Select[t, First@# < 350 &]; Sort[ Fibonacci[ #[[1]]]/Fibonacci[ #[[2]]] & /@ u] (* Robert G. Wilson v, Oct 21 2010 *)

a(11) onwards from Robert G. Wilson v, Oct 21 2010

cp's OEIS Frontend

A145275 a(n) = A145232(n+1)/A145232(n).

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A145274 a(n) = A145231(n+1)/A145231(n).

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A145276 a(n) = A145233(n+1)/A145233(n).

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A181419 Numbers of the form Fibonacci(p^{k+1})/Fibonacci(p^k) where p are primes, k>=1.

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