A090819 -id:A090819 - cp's OEIS frontend

A134787 Numbers k such that Fibonacci(prime(k)) is not prime.

1, 8, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86

Offset: 1

Artur Jasinski, Nov 12 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000720 (pi), A050937, A090819.

[n: n in [1..100]| not IsPrime(Fibonacci(NthPrime(n)))]; // Vincenzo Librandi, Jan 18 2013

k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, n]], {n, 1, 100}]; k
Select[Range[90],!PrimeQ[Fibonacci[Prime[#]]]&] (* Harvey P. Dale, Oct 16 2016 *)

is(n)=!isprime(fibonacci(prime(n))) \\ Charles R Greathouse IV, Feb 03 2014

a(n) = pi(A090819(n)). - Amiram Eldar, Oct 25 2024

Definition corrected by N. J. A. Sloane, Nov 12 2007

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 *)

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

A135958 a(n) = smallest prime p such that Fibonacci(p) has exactly n prime factors.

Original entry on oeis.org

2, 3, 19, 37, 97, 229, 503, 367, 971

Offset: 0

Artur Jasinski, Dec 08 2007

A135959 gives the Fibonacci numbers. Cf. A000045, A050937, A075737, A090819, A135957.

a(n) = {p = 2; while (omega(fibonacci(p)) != n, p = nextprime(p+1)); p;} \\ Michel Marcus, Nov 08 2013

a(n) = prime(A135957(n)).

Edited and extended by David Wasserman, Mar 26 2008

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

A134787 Numbers k such that Fibonacci(prime(k)) is not prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

Extensions

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A135958 a(n) = smallest prime p such that Fibonacci(p) has exactly n prime factors.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

Extensions

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