A134787 -id:A134787 - cp's OEIS frontend

A090819 Primes p such that the p-th Fibonacci number is nonprime.

2, 19, 31, 37, 41, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 109, 113, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349

Offset: 1

Cino Hilliard, Feb 11 2004

Is it true that a(n) ~ n log n? - Charles R Greathouse IV, Aug 15 2015

			Fibonacci(37) = 24157817 = 73*149*2221. [corrected by _Bobby Jacobs_, Sep 25 2017]

Cf. A000045, A001605, A134787.

Essentially the same as A038672.

Select[Prime[Range[62]], ! PrimeQ[Fibonacci[#]] &] (* Jayanta Basu, Jul 10 2013 *)

f(n) = forprime(x=2,n,p=fibonacci(x);if(!isprime(p),print1(x",")))

a(n) = prime(A134787(n)). - Amiram Eldar, Oct 25 2024

Definition corrected by Don Reble, Sep 04 2008

A134852 Number of distinct prime factors of the Fibonacci numbers in A050937.

Original entry on oeis.org

0, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 3, 4, 2, 4, 4, 2, 2, 3, 3, 2, 2, 4, 2, 4, 4, 2, 5, 3, 4, 3, 2, 3, 3, 4, 2, 2, 3, 4, 2, 4, 4, 4, 3, 2, 3, 5, 4, 2, 7, 5, 4, 3, 3, 2, 2, 4, 3, 4, 5, 5, 3, 5, 3, 2, 3, 4, 3, 4, 6, 3, 4, 3, 5, 3, 5, 6, 2

Offset: 1

Artur Jasinski, Nov 13 2007

nonn

Charles R Greathouse IV and Amiram Eldar, Table of n, a(n) for n = 1..202 (terms 1..185 from Charles R Greathouse IV)

Cf. A000045, A001221, A001605, A050937, A075737, A090819, A134787, A134851.

a = {}; k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; AppendTo[k, c]], {n, 1, 50}]; k

forprime(p=2,99,t=omega(fibonacci(p)); if(t!=1,print1(t", "))) \\ Charles R Greathouse IV, Feb 03 2014

a(n) = A001221(A050937(n)). - R. J. Mathar, May 03 2008

Edited by R. J. Mathar, May 03 2008

a(38)-a(87) from Charles R Greathouse IV, Feb 03 2014

A134851 Number of primes between A001605(n) and A001605(n+1).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 2, 1, 4, 1, 8, 9, 1, 39, 11, 1, 3, 10, 7, 1, 324, 208, 73, 442, 42, 498, 1122, 502, 508, 147, 1235, 2796, 2014, 2145, 1520, 4388, 15584, 2814, 11888, 274, 826, 24119, 8554, 16877, 24680, 11591, 11503, 63625, 22803, 6374, 92008, 115147, 79772, 157711, 3110

Offset: 1

Artur Jasinski, Nov 13 2007

nonn

Cf. A000045, A000720, A001605, A050937, A075737, A090819, A134787.

a = {}; k = {}; Do[If[PrimeQ[Fibonacci[n]], AppendTo[k, n]], {n, 1, 1000}]; Do[AppendTo[a, PrimePi[k[[n + 1]]] - PrimePi[k[[n]]]], {n, 1, 20}]; a

a(n) = primepi(A001605(n+1)) - primepi(A001605(n)). - Amiram Eldar, Sep 01 2019

More terms from Amiram Eldar, Sep 01 2019 and Sep 15 2024

A135953 (Nonprime Fibonacci numbers with prime indices) that have exactly 2 prime factors.

Original entry on oeis.org

4181, 1346269, 165580141, 53316291173, 956722026041, 2504730781961, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 573147844013817084101, 10284720757613717413913, 26925748508234281076009

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

Conjecture: All numbers in this sequence are products of two sums of two squares, e.g. 4181 = 37*113 = (1^2+6^2)*(7^2+8^2), 1346269 = 557*2417 = (14^2+19^2)*(4^2+49^2).

Amiram Eldar, Table of n, a(n) for n = 1..42

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135954, A135955, A135956, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 2, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k
Select[Fibonacci[Prime[Range[30]]],PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 18 2012 *)

A135957 a(n) = smallest k such that Fibonacci(prime(k)) has exactly n prime factors.

Original entry on oeis.org

1, 2, 8, 12, 25, 50, 96, 73, 164

Offset: 0

Artur Jasinski, Dec 08 2007

A135958 gives prime(k). Cf. A000045, A001605, A050937, A075737, A134787, A134852.

Edited and extended by David Wasserman, Mar 26 2008

A135956 Members of A050937 (nonprime Fibonacci numbers with prime index) with 5 or more distinct prime factors.

Original entry on oeis.org

322615043836854783580186309282650000354271239929, 1476475227036382503281437027911536541406625644706194668152438732346449273, 22334640661774067356412331900038009953045351020683823507202893507476314037053

Offset: 1

Artur Jasinski, Dec 08 2007

Conjecture: all numbers in this sequence are product of 5 or more sum of two squares

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135954, A135955, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; Print[n]; If[c > 4, Print[Fibonacci[Prime[n]]]; AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 100}]; k

A050937 INTERSECT { A051270 UNION A074969 UNION ... } = A050937 MINUS {A135955 UNION A135954 UNION A135953}. - R. J. Mathar, Jun 09 2008

Edited by R. J. Mathar, Jun 09 2008

A135954 Nonprime Fibonacci numbers with prime indices (A050937) that have exactly 3 prime factors.

Original entry on oeis.org

24157817, 44945570212853, 1500520536206896083277, 50095301248058391139327916261, 11463113765491467695340528626429782121, 30010821454963453907530667147829489881, 2211236406303914545699412969744873993387956988653, 103881042195729914708510518382775401680142036775841

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

Conjecture: All numbers in this sequence are products of three sums of two squares.

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135955, A135956, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 3, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k

f(n) = forprime(x=2, n, p=fibonacci(x); if(!isprime(p) && omega(p) == 3, print1(p", "))) \\ Georg Fischer, Feb 15 2025

a(6)-a(8) from Georg Fischer, Feb 15 2025

A135955 (Nonprime Fibonacci numbers with prime indices, A050937) which have exactly 4 prime factors.

Original entry on oeis.org

83621143489848422977, 6161314747715278029583501626149, 289450641941273985495088042104137, 5193981023518027157495786850488117, 66233869353085486281758142155705206899077

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

Conjecture: All numbers in this sequence are products of four sums of two squares.

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135953, A135954, A135956, A135957.

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 4, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k

A134788 If Fibonacci(prime(k)) is prime, append Fibonacci(prime(k)) - prime(k) to the sequence.

Original entry on oeis.org

-1, 0, 6, 78, 220, 1580, 28634, 514200, 433494394, 2971215026, 99194853094755414, 1066340417491710595814572038, 19134702400093278081449423780, 475420437734698220747368027166749382927701417016557193662268716376935475882

Offset: 1

Artur Jasinski, Nov 12 2007

sign

Amiram Eldar, Table of n, a(n) for n = 1..20

Cf. A050937, A090819, A134787.

k = {}; Do[If[PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, Fibonacci[Prime[n]] - Prime[n]]], {n, 1, 100}]; k
fpn[n_]:=Module[{prn=Prime[n],fib},fib=Fibonacci[prn];If[PrimeQ[fib], fib- prn,a]]; DeleteCases[Table[fpn[i],{i,100}],a] (* Harvey P. Dale, Mar 27 2012 *)

forprime(n=1,1000,if(isprime(fibonacci(n)),print1(fibonacci(n)-n,","))) \\ Edward Jiang, Nov 23 2013

A134789 a(n) = round(Fibonacci(prime(k))/prime(k)), where k = A119984(n).

Original entry on oeis.org

1, 1, 2, 8, 18, 94, 1246, 17732, 10081266, 63217342, 1195118711985006, 8140003186959622868813528, 139669360584622467747806014, 1324290912910022899017738237233285189213652972190967113265372469016533360

Offset: 1

Artur Jasinski, Nov 12 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..22

Cf. A000045, A050937, A090819, A119984, A134787, A134788.

k = {}; Do[If[PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, Round[Fibonacci[Prime[n]]/Prime[n]]]], {n, 1, 100}]; k

cp's OEIS Frontend

A090819 Primes p such that the p-th Fibonacci number is nonprime.

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A134852 Number of distinct prime factors of the Fibonacci numbers in A050937.

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A134851 Number of primes between A001605(n) and A001605(n+1).

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A135953 (Nonprime Fibonacci numbers with prime indices) that have exactly 2 prime factors.

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A135957 a(n) = smallest k such that Fibonacci(prime(k)) has exactly n prime factors.

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A135956 Members of A050937 (nonprime Fibonacci numbers with prime index) with 5 or more distinct prime factors.

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A135954 Nonprime Fibonacci numbers with prime indices (A050937) that have exactly 3 prime factors.

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A135955 (Nonprime Fibonacci numbers with prime indices, A050937) which have exactly 4 prime factors.

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Mathematica

A134788 If Fibonacci(prime(k)) is prime, append Fibonacci(prime(k)) - prime(k) to the sequence.

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