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 1-10 of 22 results. Next

A134850 Number of primes between A075737(n) and A075737(n+1), including one bound.

Original entry on oeis.org

2, 3, 18, 27, 200, 2870, 39492, 22980943, 120106923, 2602986018837012
Offset: 1

Views

Author

Artur Jasinski, Nov 13 2007

Keywords

Links

Crossrefs

Cf. A000045, A050937, A075737, A090819, A134787, A307499.

Programs

  • Mathematica
    a = {}; k = {}; Do[If[PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, Fibonacci[Prime[n]]]], {n, 1, 100}];Do[AppendTo[a, PrimePi[k[[n + 1]]] - PrimePi[k[[n]]]], {n, 1, 9}]; a

Extensions

Edited by N. J. A. Sloane, Oct 07 2008
a(10) using Kim Walisch's primecount, from Amiram Eldar, May 14 2023

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

Views

Author

Artur Jasinski, Nov 13 2007

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    a = {}; k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; AppendTo[k, c]], {n, 1, 50}]; k
  • PARI
    forprime(p=2,99,t=omega(fibonacci(p)); if(t!=1,print1(t", "))) \\ Charles R Greathouse IV, Feb 03 2014

Formula

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

Extensions

Edited by R. J. Mathar, May 03 2008
a(38)-a(87) from Charles R Greathouse IV, Feb 03 2014

A119984 Numbers k such that Fibonacci(prime(k)) is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 9, 10, 14, 15, 23, 32, 33, 72, 83, 84, 87, 97, 104, 105, 429, 637, 710, 1152, 1194, 1692, 2814, 3316, 3824, 3971, 5206, 8002, 10016, 12161, 13681, 18069, 33653, 36467, 48355, 48629, 49455, 73574, 82128, 99005, 123685, 135276, 146779, 210404, 233207, 239581
Offset: 1

Views

Author

Alexander Adamchuk, Aug 04 2006

Keywords

Comments

All prime Fibonacci numbers have prime indices, except prime F(4) = 3; a(n) is such that Fibonacci(prime(a(n))) is prime. - Robert G. Wilson v, Aug 05 2006

Links

Crossrefs

Cf. A000045, A000720, A001605, A005478, A030426, A075737, A083668.

Programs

  • Mathematica
    Select[ Range@3000, PrimeQ@ Fibonacci@ Prime@ # &] (* Robert G. Wilson v, Aug 05 2006 *)

Formula

a(n) = pi(A001605(n+1)). This holds for all n including n=1, since pi(4) = pi(3) = 2. - Jens Kruse Andersen, Jul 24 2014

Extensions

a(21)-a(27) from Robert G. Wilson v, Aug 05 2006
More terms (from A001605) from T. D. Noe, Aug 18 2006
a(42)-a(48) (from A001605, found by Henri Lifchitz) from Jens Kruse Andersen, Jul 24 2014
a(49)-a(50) (from A001605, found by Henri Lifchitz) from Amiram Eldar, Sep 01 2019

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

Views

Author

Artur Jasinski, Nov 13 2007

Keywords

Crossrefs

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

Programs

  • Mathematica
    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

Formula

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

Extensions

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

Views

Author

Artur Jasinski, Dec 08 2007

Keywords

Comments

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).

Links

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Artur Jasinski, Dec 08 2007

Keywords

Crossrefs

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

Extensions

Edited and extended by David Wasserman, Mar 26 2008

A083668 Prime indices of prime Fibonacci numbers.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571, 2971, 4723, 5387, 9311, 9677, 14431, 25561, 30757, 35999, 37511, 50833, 81839, 104911, 130021, 148091, 201107, 397379, 433781, 590041, 593689, 604711, 931517, 1049897, 1285607, 1636007, 1803059, 1968721
Offset: 1

Views

Author

Cino Hilliard, Jun 14 2003

Keywords

Comments

Same as A001605 without the number 4.
From V. Raman, Oct 04 2012: (Start)
Also the indices of prime Fibonacci numbers which can be written as the sum of two positive squares.
The Fibonacci numbers F(6k+1) and F(6k+5) are congruent to 1 (mod 4).
(End)

Examples

			For Fib(n) to be prime, n must be prime, except for n=4. The first 9 primes are: 2, 3, 5, 7, 11, 13, 17, 19 and 23. The corresponding Fibonacci numbers are: 1, 2, 5, 13, 89, 233, 1597, 4181 and 28657. All of these are prime except Fib(2) = 1 and Fib(19) = 4181. So the first 7 terms of this sequence are 3, 5, 7, 11, 13, 17 and 23.

Crossrefs

Cf. A001605, A075737.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ Fibonacci[ Prime[n]]], Print[ Prime[n]]], {n, 1, 1000}]
  • PARI
    pif(n) = { forprime(x=2,n, if(isprime(fibonacci(x)), print1(x" "))) }
  • PARI
    is(p)=isprime(p) & ispseudoprime(fibonacci(p))  \\ Charles R Greathouse IV, Sep 19 2012

Extensions

More terms from Zak Seidov, Aug 31 2006
Replaced the erroneous example Harry J. Smith, Jan 16 2009
Terms a(42) to a(47) added by V. Raman, Oct 04 2012
Definition and wrong statement in example corrected by M. F. Hasler, Oct 08 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

Views

Author

Artur Jasinski, Dec 08 2007

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    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

Formula

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

Extensions

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

Views

Author

Artur Jasinski, Dec 08 2007

Keywords

Comments

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

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Artur Jasinski, Dec 08 2007

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    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
Showing 1-10 of 22 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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