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.

A115312 a(n) = gcd(Lucas(n)-1, Fibonacci(n)+1).

Original entry on oeis.org

2, 2, 3, 2, 2, 1, 14, 2, 5, 2, 18, 1, 26, 2, 47, 2, 34, 1, 246, 2, 89, 2, 322, 1, 466, 2, 843, 2, 610, 1, 4414, 2, 1597, 2, 5778, 1, 8362, 2, 15127, 2, 10946, 1, 79206, 2, 28657, 2, 103682, 1, 150050, 2, 271443, 2, 196418, 1, 1421294, 2, 514229, 2, 1860498, 1
Offset: 1

Views

Author

Giovanni Resta, Jan 20 2006

Keywords

Comments

Here Lucas is: Lucas(1)=1, Lucas(2)=3 and, for n>2, Lucas(n) = Lucas(n-1) + Lucas(n-2). See A000032.
a(n) is prime for n = 1, 2, 3, 4, 5, 8, 9, 10, 14, 15, 16, 20, 21, 22, 26, 28, 32, 33, 34, 38, 40, 44, 45, ... - Vincenzo Librandi, Dec 24 2015
350 of the first 1000 terms are primes. - Harvey P. Dale, Mar 25 2020

Examples

			a(15) = 47 since F(15) + 1 =13*47 and L(15) - 1 = 29*47.

Links

Crossrefs

Cf. A000032, A000045, A111956, A115311, A115313, A115314.

Programs

  • Magma
    [Gcd(Lucas(n)-1, Fibonacci(n)+1): n in [1..60]]; // Vincenzo Librandi, Dec 24 2015
  • Mathematica
    lucas[1]=1; lucas[2]=3; lucas[n_]:= lucas[n]= lucas[n-1] + lucas[n-2]; Table[GCD[lucas[i]-1, Fibonacci[i]+1], {i, 60}]
GCD[#[[1]]-1,#[[2]]+1]&/@With[{nn=60},Thread[{LucasL[Range[ nn]],Fibonacci[ Range[nn]]}]] (* Harvey P. Dale, Mar 25 2020 *)
  • PARI
    a(n) = gcd(fibonacci(n+1)+fibonacci(n-1)-1,fibonacci(n)+1); \\ Altug Alkan, Dec 24 2015

A115314 a(n) = gcd(Lucas(n)+1, Fibonacci(n)-1).

Original entry on oeis.org

2, 4, 1, 2, 4, 1, 6, 4, 11, 2, 8, 1, 58, 4, 21, 2, 76, 1, 110, 4, 199, 2, 144, 1, 1042, 4, 377, 2, 1364, 1, 1974, 4, 3571, 2, 2584, 1, 18698, 4, 6765, 2, 24476, 1, 35422, 4, 64079, 2, 46368, 1, 335522, 4, 121393, 2, 439204, 1, 635622, 4, 1149851, 2, 832040, 1
Offset: 1

Views

Author

Giovanni Resta, Jan 20 2006

Keywords

Comments

Here Lucas is: Lucas(1)=1, Lucas(2)=3 and, for n>2, Lucas(n) = Lucas(n-1) + Lucas(n-2). See A000032.
a(n) is prime for n = 1, 4, 9, 10, 16, 21, 22, 28, 33, 34, 40, 46, 52, 58, 64, 70, 76, 81, 82, 88, 93, 94, ... - Vincenzo Librandi, Dec 24 2015

Examples

			a(15) = 21 = 3*7 since F(15) - 1 = 3*7*29 and L(15) + 1 = 3*5*7*13.

Links

Crossrefs

Cf. A000032, A000045, A111956, A115311, A115312, A115313.

Programs

  • Magma
    [Gcd(Lucas(n)+1, Fibonacci(n)-1): n in [1..60]]; // Vincenzo Librandi, Dec 24 2015
  • Mathematica
    lucas[1]=1; lucas[2]=3; lucas[n_]:= lucas[n]= lucas[n-1] + lucas[n-2]; Table[GCD[lucas[i]+1, Fibonacci[i]-1], {i, 60}]
Module[{nn=60,l,f},l=LucasL[Range[nn]]+1;f=Fibonacci[Range[nn]]-1;GCD@@@ Thread[ {l,f}]] (* Harvey P. Dale, Apr 29 2020 *)
  • PARI
    a(n) = gcd(fibonacci(n+1)+fibonacci(n-1)+1,fibonacci(n)-1); \\ Altug Alkan, Dec 24 2015

A115313 a(n) = gcd(Lucas(n)+1, Fibonacci(n)+1).

Original entry on oeis.org

2, 2, 1, 4, 6, 1, 2, 2, 7, 4, 10, 1, 18, 2, 13, 4, 94, 1, 34, 2, 123, 4, 178, 1, 322, 2, 233, 4, 1686, 1, 610, 2, 2207, 4, 3194, 1, 5778, 2, 4181, 4, 30254, 1, 10946, 2, 39603, 4, 57314, 1, 103682, 2, 75025, 4, 542886, 1, 196418, 2, 710647, 4, 1028458, 1
Offset: 1

Views

Author

Giovanni Resta, Jan 20 2006

Keywords

Comments

Here Lucas is: Lucas(1)=1, Lucas(2)=3 and, for n>2, Lucas(n) = Lucas(n-1)+Lucas(n-2). See A000032.
a(n) is prime for n = 1, 2, 7, 8, 9, 14, 15, 20, 26, 27, 32, 33, 38, 44, 50, 56, 62, 68, 74, 80, 86, 87, ... - Vincenzo Librandi, Dec 24 2015

Examples

			a(15) = 13 since F(15) + 1 = 13*47 and L(15) + 1 = 3*5*7*13.

Crossrefs

Cf. A000032, A000045, A111956, A115311, A115312, A115314.

Programs

  • Magma
    [Gcd(Lucas(n)+1, Fibonacci(n)+1): n in [1..60]]; // Vincenzo Librandi, Dec 24 2015
  • Mathematica
    lucas[1]=1; lucas[2]=3; lucas[n_]:= lucas[n]= lucas[n-1] + lucas[n-2]; Table[GCD[lucas[i]+1, Fibonacci[i]+1], {i, 60}]
  • PARI
    a(n) = gcd(fibonacci(n+1)+fibonacci(n-1)+1,fibonacci(n)+1); \\ Altug Alkan, Dec 24 2015
Showing 1-3 of 3 results.

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