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 1-7 of 7 results.

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).

Crossrefs

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 *)

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

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

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

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

A135968 Sum of the distinct prime factors of the Fibonacci number A050937(n).

Original entry on oeis.org

0, 150, 2974, 2443, 62158, 55946694, 2710261050, 555008010, 1547031, 46165377746, 95396546, 92180471494910, 1665088321801550, 364125780, 771601497990, 518283023, 8242065051309594, 32530503217194, 272602401466814027806, 5568053048227732238014, 85526725052226871
Offset: 1

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Examples

			a(2) = 150 = 37+113 because A050937(2) = 4181 = 37*113.
a(3) = 2974 = 557 + 2417 because A050937(3) = 1346269 = 557*2417.
		

Crossrefs

Programs

  • Mathematica
    k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], b = FactorInteger[Fibonacci[Prime[n]]]; c =Length[FactorInteger[b]]; d = 0; Do[d = d + b[[r]][[1]], {r, 1, c}]; AppendTo[k, d]], {n, 1, 50}]; k

Formula

a(n) = A008472(A050937(n)). - R. J. Mathar, Dec 12 2007

Extensions

Edited by R. J. Mathar, Dec 12 2007
a(19)-a(21) from Amiram Eldar, Oct 13 2024

A135969 Sum of the prime factors of A135953(n).

Original entry on oeis.org

150, 2974, 62158, 55946694, 2710261050, 555008010, 46165377746, 95396546, 92180471494910, 1665088321801550, 771601497990, 8242065051309594, 32530503217194, 272602401466814027806, 5568053048227732238014, 2811666624525811646469921614, 1966344318693363713266514
Offset: 1

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Comments

A subsequence of A135968.

Examples

			a(1) = 150 = 37+113 because A135953(1) = 4181 = 37*113.
a(2) = 2974 = 557+2417 because A135953(2) = 1346269 = 557*2417.
		

Crossrefs

Programs

  • Mathematica
    k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], b = FactorInteger[Fibonacci[Prime[n]]]; c = Length[FactorInteger[b]]; If[c == 2, d = b[[1]][[1]] + b[[2]][[1]]; AppendTo[k, d]]], {n, 1, 50}]; k
    Total[Transpose[FactorInteger[#]][[1]]]&/@Select[Fibonacci[Prime[ Range[50]]], PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 18 2012 *)

Formula

a(n) = A008472(A135953(n)). - R. J. Mathar, Nov 26 2008

Extensions

Definition clarified by R. J. Mathar, Nov 26 2008
a(16)-a(17) from Amiram Eldar, Oct 23 2024

A135960 Indices where records occur in A134852.

Original entry on oeis.org

1, 2, 4, 14, 37, 59, 144, 173
Offset: 1

Views

Author

Artur Jasinski, Dec 08 2007

Keywords

Crossrefs

Extensions

a(7)-a(8) from Amiram Eldar, Sep 01 2019 (calculated from the b-file at A134852)

A135970 Fibonacci(Mersenne primes): a(n) = Fibonacci(A000668(n)).

Original entry on oeis.org

2, 13, 1346269, 155576970220531065681649693
Offset: 1

Views

Author

Artur Jasinski, Dec 09 2007

Keywords

Comments

This sequence is a subsequence of A101342. The next term, a(5), has 1712 digits.

Crossrefs

Programs

  • Mathematica
    k = {}; Do[If[PrimeQ[2^n - 1], AppendTo[k, Fibonacci[2^n - 1]]], {n, 1, 15}]; k
    Fibonacci/@Select[Table[2^Prime[n]-1,{n,5}],PrimeQ] (* Harvey P. Dale, May 06 2018 *)
Showing 1-7 of 7 results.