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 1-2 of 2 results.

A113188 Primes that are the difference of two Fibonacci numbers; primes in A007298.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 19, 29, 31, 47, 53, 89, 131, 139, 199, 233, 521, 607, 953, 1453, 1597, 2207, 2351, 2579, 3571, 6763, 9349, 10891, 28513, 28649, 28657, 42187, 44771, 46279, 75017, 189653, 317777, 514229, 1981891, 2177699, 3010349, 3206767
Offset: 1

Views

Author

T. D. Noe, Oct 17 2005

Keywords

Comments

The difference F(i)-F(j) equals the sum F(j-1)+...+F(i-2) [Corrected by Patrick Capelle, Mar 01 2008]. In general, we need gcd(i,j)=1 for F(i)-F(j) to be prime. The exceptions are handled by the following rule: if i and j are both even or both odd, then F(i)-F(j) is prime if either (1) i-j=4 and L(i-2) is a Lucas prime or (2) i-j=2 and F(i-1) is a Fibonacci prime.

Examples

			The prime 139 is here because it is F(12)-F(5).

Links

Crossrefs

Cf. A000045 (Fibonacci numbers), A001605 (Fibonacci(n) is prime), A001606 (Lucas(n) is prime), A113189 (number of times that Fibonacci(n)-Fibonacci(i) is prime for i=0..n-3).

Programs

  • Mathematica
    lst={}; Do[p=Fibonacci[n]-Fibonacci[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, n-1}]; Union[lst]
Select[Union[Flatten[Differences/@Subsets[Fibonacci[Range[50]],{2}]]],PrimeQ] (* Harvey P. Dale, Aug 04 2024 *)
  • PARI
    list(lim)=my(v=List(),F=vector(A130233(lim),i,fibonacci(i)),s,t); for(i=1,#F, s=0; forstep(j=i,1,-1, s+=F[j]; if(s>lim, break); if(isprime(s), listput(v,s)))); Set(v) \\ Charles R Greathouse IV, Oct 07 2016

A113190 Numbers n such that Fibonacci(n)-Fibonacci(i) is composite for all i=0..n-3.

Original entry on oeis.org

14, 22, 26, 30, 31, 34, 38, 40, 42, 44, 46, 54, 61, 62, 64, 65, 67, 78, 80, 82, 88, 92, 94, 95, 98, 102, 103, 109, 112, 113, 117, 119, 121, 122, 125, 126, 127, 134, 135, 138, 139, 142, 143, 152, 154, 155, 158, 166, 167, 170, 172, 174, 175, 176, 182, 188, 190, 193
Offset: 1

Views

Author

T. D. Noe, Oct 17 2005

Keywords

Comments

These are the n such that A113189(n)=0.

Crossrefs

Cf. A113188 (primes that are the difference of two Fibonacci numbers).

Programs

  • Mathematica
    lst={}; Do[i=0; While[iHarvey P. Dale, Nov 05 2017 *)
Showing 1-2 of 2 results.

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

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