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 1-4 of 4 results.

A050180 Numbers m such that prime(m) + Fibonacci(m) is prime.

Original entry on oeis.org

1, 3, 12, 24, 42, 60, 132, 303, 312, 450, 564, 1236, 1419, 2952, 10098, 12060, 13848, 17229, 22356, 37896, 251904
Offset: 1

Views

Author

Jason Earls, Oct 06 2001

Keywords

Comments

a(22) > 256737. - J.W.L. (Jan) Eerland, Jun 22 2022

Crossrefs

Cf. A004397, A001605.

Programs

  • Magma
    [n: n in [1..2000] | IsPrime(NthPrime(n)+Fibonacci(n))]; // Vincenzo Librandi, Jul 29 2016
  • Mathematica
    Do[ If[ PrimeQ[ Prime[n] + Fibonacci[n]], Print[n] ], {n, 1, 150000} ]
Select[Range[10000], PrimeQ[Fibonacci[#] + Prime[#]] &] (* Vincenzo Librandi, Jul 29 2016 *)
DeleteCases[ParallelTable[If[PrimeQ[Prime[n]+Fibonacci[n]],n,a],{n,0,256737}],a] (* J.W.L. (Jan) Eerland, Jun 22 2022 *)
  • PARI
    for(n=1,10^5, if(isprime(prime(n)+fibonacci(n)),print1(n," ")))

Extensions

More terms from Robert G. Wilson v, Oct 08 2001
a(18)-a(19) from Vincenzo Librandi, Apr 10 2020
a(20) from J.W.L. (Jan) Eerland, Dec 23 2021
a(21) from J.W.L. (Jan) Eerland, Jun 22 2022

A100700 n-th Fibonacci number minus n-th prime number.

Original entry on oeis.org

-1, -2, -3, -4, -6, -5, -4, 2, 11, 26, 58, 107, 192, 334, 563, 934, 1538, 2523, 4114, 6694, 10873, 17632, 28574, 46279, 74928, 121292, 196315, 317704, 514120, 831927, 1346142, 2178178, 3524441, 5702748, 9227316, 14930201, 24157660, 39088006, 63245819
Offset: 1

Views

Author

Alonso del Arte, Dec 09 2004

Keywords

Examples

			a(12) = 107 because the 12th Fibonacci number is 144, the 12th prime number is 37 and 144 - 37 = 107.

Links

Crossrefs

Cf. A004397, A064497.

Programs

  • Magma
    [Fibonacci(n) - NthPrime(n): n in [1..40]]; // Vincenzo Librandi, May 20 2016
  • Mathematica
    Table[Fibonacci[n] - Prime[n], {n, 35}]

A113753 a(n) = Fibonacci(n-1) + prime(n).

Original entry on oeis.org

2, 4, 6, 9, 14, 18, 25, 32, 44, 63, 86, 126, 185, 276, 424, 663, 1046, 1658, 2651, 4252, 6838, 11025, 17794, 28746, 46465, 75126, 121496, 196525, 317920, 514342, 832167, 1346400, 2178446, 3524717, 5703036, 9227616, 14930509, 24157980, 39088336
Offset: 1

Views

Author

Mark Dowdey (mdowdey(AT)comcast.net), Jan 18 2006

Keywords

Examples

			a(4) = 9 because the 4th prime is 7 and F(4) is 2. a(4) = 7 + 2 = 9.

Links

Crossrefs

Cf. A000040, A000045, A004397.

Programs

  • Maple
    with(combinat, fibonacci): for n to 10^3 do print(fibonacci(n - 1) + ithprime(n)) end do; # Reza K Ghazi, May 14 2021
  • Mathematica
    Do[Print[Fibonacci[n - 1] + Prime[n]], {n, 10^3}] (* Reza K Ghazi, May 14 2021*)
  • PARI
    for(n=1, 1e3, print1(fibonacci(n-1)+prime(n)", ")) \\ Reza K Ghazi, May 14 2021
  • SageMath
    p = 0
for n in range(1, 10^3+1):
    print(fibonacci(n-1) + next_prime(p))
    p = next_prime(p) # Reza K Ghazi, May 14 2021

Extensions

Name corrected by Reza K Ghazi, May 15 2021

A261543 Numbers of the form (prime(k) + Fibonacci(k))/2.

Original entry on oeis.org

2, 5, 8, 15, 20, 42, 60, 137, 210, 520, 828, 2124, 3418, 8895, 14370, 37561, 60747, 158959, 257169, 673198, 1089220, 2851513, 4613807, 12078987, 19544166, 51167164, 82790160, 216747314, 350704463, 918156051, 1485607642, 3889371138, 6293134627
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 24 2015

Keywords

Comments

The numbers represented as the arithmetic mean of the Fibonacci numbers and prime numbers with identical indices.

Examples

			a(1) = (prime(2) + Fibonacci(2))/2 = (3 + 1)/2 = 2.

Links

Crossrefs

Cf. A000040, A000045, A004397, A001651.

Programs

Formula

a(n) = (prime(A001651(n + 1)) + Fibonacci(A001651(n + 1)))/2
Showing 1-4 of 4 results.

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

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