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.

A175404 Numbers k with property that k + Fibonacci(k) is prime.

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 28, 33, 38, 808, 1642, 13288, 20434, 29001, 57374, 121858
Offset: 1

Views

Author

Zak Seidov, May 01 2010

Keywords

Comments

Next term > 49000. - Robert G. Wilson v, Jun 12 2010

Crossrefs

Cf. A000045 = Fibonacci(n), A069108 = Primes of the form k + Fibonacci(k).

Programs

  • Mathematica
    fQ[n_] := PrimeQ[ Fibonacci@n + n]; lst = {}; k = 1; While[k < 50001, If[fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst (* Robert G. Wilson v, Jun 12 2010 *)
Select[Range[2000],PrimeQ[#+Fibonacci[#]]&] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Mar 21 2024 *)
  • PARI
    isok(n) = isprime(n + fibonacci(n)); \\ Michel Marcus, Mar 30 2016

Extensions

a(12)-a(14) from Robert G. Wilson v, Jun 12 2010
a(15)-a(16) from Michael S. Branicky, Aug 01 2024

A173684 Semiprimes of the form Fibonacci(k) + k.

Original entry on oeis.org

10, 14, 65, 391, 1003, 2602, 10967, 2178341, 701408777, 86267571326, 591286729937, 4052739537943, 72723460248209, 117669030461063, 3416454622906783, 61305790721611673, 420196140727489759, 2427893228399975082557, 251728825683549488150424389
Offset: 1

Views

Author

Jonathan Vos Post, Jan 26 2011

Keywords

Comments

This is to A069108 as semiprimes are to primes. A002062(k) is semiprime for k = 5, 6, 10, 14, 16, 18, 21, 32, ...

Examples

			F(21) + 21 = 10967 = 11 * 997, thus 10967 is in the sequence.

Links

Crossrefs

Cf. A000045, A001358, A002062, A053409, A069108.

Programs

  • Magma
    IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ a: n in [1..100] | IsSemiprime(a) where a is n+Fibonacci(n) ]; // Klaus Brockhaus, Jan 27 2011
  • Mathematica
    Select[Table[Fibonacci[n]+n,{n,200}],PrimeOmega[#]==2&] (* Harvey P. Dale, Nov 02 2011 *)

Formula

A002062 INTERSECTION A001358.
Showing 1-2 of 2 results.

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

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