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 1-3 of 3 results.

A099381 Numbers n such that |Fibonacci(n) - prime(n)| is prime.

Original entry on oeis.org

2, 3, 6, 8, 9, 12, 15, 24, 33, 48, 225, 525, 948, 1344, 5169, 30600, 32520, 32604, 72396
Offset: 1

Views

Author

Rick L. Shepherd, Nov 16 2004

Keywords

Comments

Fibonacci(n) - prime(n) > 0 for n >= 8. All terms other than 2 and 8 (only two terms producing 2, the only even prime) are divisible by 3 (as Fibonacci(n) is even - and hence |Fibonacci(n) - prime(n)| > 1 and odd - iff n is divisible by 3).
Some of the larger entries may only correspond to probable primes.

Examples

			9 is a term as Fibonacci(9) - prime(9) = 34 - 23 = 11, a prime.
		

Crossrefs

Cf. A050180 (Fibonacci(n) + prime(n) is prime).

Programs

  • Mathematica
    fQ[n_] := PrimeQ[ Fibonacci[n] - Prime[n]]; Do[ If[ fQ[n], Print[n]], {n, 9, 10^4, 3}] (* Robert G. Wilson v, Nov 18 2004 *)
  • PARI
    print1(2,",",3,",",6,",",8,","); forstep(n=9,5169,3, if(isprime(fibonacci(n)-prime(n)), print1(n,",")))

Extensions

4 more terms from Jason Earls, Nov 25 2007

A288794 Numbers k such that Lucas(k) + prime(k) is a prime.

Original entry on oeis.org

1, 6, 12, 18, 54, 75, 354, 10158, 23280, 33726, 38226, 70749, 244779, 308604
Offset: 1

Views

Author

Vincenzo Librandi, Jun 16 2017

Keywords

Comments

a(15) > 500000.

Examples

			a(1) = 1 because Lucas(1)=1, prime(1)=2 and 1+2=3 is a prime.
a(2) = 6 because Lucas(6)=18, prime(6)=13 and 18+13=31 is a prime.
		

Crossrefs

Programs

  • Magma
    [n: n in [1..950] | IsPrime(Lucas(n)+NthPrime(n))];
  • Mathematica
    Select[Range[1000], PrimeQ[LucasL[#] + Prime[#]] &]

Extensions

a(8)-a(12) from Robert Price, Oct 26 2017
a(13)-a(14) from Robert Price, Dec 16 2017

A297623 Numbers k such that Lucas(k) - prime(k) is a prime.

Original entry on oeis.org

6, 9, 18, 33, 51, 54, 57, 189, 6948, 28617, 162864, 173682, 216870, 496533
Offset: 1

Views

Author

Vincenzo Librandi, Jan 06 2018

Keywords

Comments

a(15) > 5*10^5. - Robert Price, Feb 17 2018

Examples

			a(1) = 6 because Lucas(6)=18, prime(6)=13 and 18-13=5 is a prime.
		

Crossrefs

Programs

  • Magma
    [n: n in [1..5000] | IsPrime(Lucas(n)-NthPrime(n))];
  • Mathematica
    Select[Range[10000], PrimeQ[LucasL[#] - Prime[#]]&]

Extensions

a(11)-a(14) from Robert Price, Feb 17 2018
Showing 1-3 of 3 results.