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.

A005479 Prime Lucas numbers (cf. A000032).

Original entry on oeis.org

2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

It appears that a(n) is the intersection ( or a subset of the intersection ) of A113192[n], Primes that are the difference of two Lucas numbers and A113188[n], Primes that are the difference of two Fibonacci numbers, excluding A113192[1] = A113188[1] = 2. - Alexander Adamchuk, Aug 06 2006
For n>2 also: Primes which are the sum of four consecutive Fibonacci numbers, a(n) = A153867(n-2), cf. link to SeqFan list (Apr. 2014). - M. F. Hasler, Apr 24 2014
Conjectures: 7, 47 and 2207 are the only a(n) mod 10 = 7. They are also the only a(n) values where the Lucas index is not a prime. See A001606 for the Lucas index values of these primes. See A266587 for the divisibility of Lucas numbers by powers of primes. - Richard R. Forberg, Mar 24 2016

References

  • R. K. Guy, Unsolved Problems in Number Theory, Section A3.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000032, A001606, A113192, A113188.

Programs

  • Mathematica
    Select[LucasL[Range[0,250]], PrimeQ] (* Harvey P. Dale, Nov 02 2011 *)

Extensions

One further term (from the Knott web site) from Parthasarathy Nambi, Jun 27 2008

A113194 Numbers k such that Lucas(k) - Lucas(i) is composite for i=0..k-3.

Original entry on oeis.org

5, 7, 10, 17, 19, 23, 29, 31, 34, 41, 44, 49, 53, 55, 57, 62, 67, 68, 71, 75, 77, 79, 80, 87, 89, 93, 98, 100, 101, 103, 107, 109, 110, 116, 122, 124, 125, 133, 134, 135, 136, 143, 147, 154, 155, 160, 161, 164, 167, 170, 173, 177, 180, 184, 185, 188, 190, 194, 196
Offset: 1

Views

Author

T. D. Noe, Oct 17 2005

Keywords

Comments

These are the numbers k such that A113193(k) = 0.

Links

Crossrefs

Cf. A000032, A113192 (primes that are the difference of two Lucas numbers).
Cf. A113193.

Programs

  • Maple
    Luc:= 2,1,3: R:= NULL: count:= 0:
a:= 1: b:= 3:
for n from 3 while count < 100 do
  c:= a+b; a:= b; b:=c; Luc:= Luc,c;
  if ormap(isprime, [seq(c-Luc[i],i=1..n-2)]) then next fi;
  R:= R, n; count:= count+1;
od:
R; # Robert Israel, Jan 18 2023
  • Mathematica
    lst={}; Do[i=0; While[i

A113193 Number of times that Lucas(n)-Lucas(i) is prime for i=0..n-3.

Original entry on oeis.org

1, 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 1, 1, 2, 0, 1, 0, 1, 3, 1, 0, 2, 2, 1, 3, 1, 0, 1, 0, 3, 3, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 0, 4, 2, 1, 3, 0, 1, 2, 1, 0, 1, 0, 2, 0, 1, 2, 1, 3, 0, 2, 1, 2, 1, 0, 0, 2, 3, 0, 1, 1, 3, 0, 1, 0, 1, 0, 0, 4, 1, 1, 1, 2, 1, 0, 1, 0, 3, 1, 1, 0, 2, 4, 1, 1, 0, 3, 0, 0, 5, 0, 1, 2, 1, 0
Offset: 3

Views

Author

T. D. Noe, Oct 17 2005

Keywords

Comments

We exclude i=n-2 and i=n-1 because they yield Lucas(n-2) and Lucas(n-1), respectively. Sequence A113194 lists the n for which a(n)=0.

Crossrefs

Cf. A113192 (primes that are the difference of two Lucas numbers).

Programs

  • Mathematica
    Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; Table[cnt=0; Do[If[PrimeQ[Lucas[n]-Lucas[i]], cnt++ ], {i, 0, n-3}]; cnt, {n, 3, 150}]
Showing 1-3 of 3 results.

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

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