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.

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A076777 Number of primes between successive Fibonacci numbers inclusive.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 2, 2, 3, 5, 8, 10, 17, 23, 37, 55, 85, 125, 198, 297, 458, 704, 1088, 1673, 2602, 4029, 6263, 9738, 15187, 23704, 36981, 57909, 90550, 142033, 222855, 349862, 549903, 865019, 1361581, 2145191, 3381318, 5334509, 8419528, 13298630, 21014892, 33227992
Offset: 0

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Author

Reinhard Zumkeller, Nov 14 2002

Keywords

Comments

a(n) = #{p prime | A000045(n)A000045(n+1)}.

Examples

			a(10) = 8, as there are 8 primes greater than A000045(10) = 55 and not greater than A000045(10+1) = 89: 59, 61, 67, 71, 73, 79, 83 and 89.

Links

Crossrefs

Cf. A000045, A000720, A054782, A082602.
Cf. A001605, A005478.

Programs

  • Maple
    with(combinat): with(numtheory): seq(pi(fibonacci(n+1))-pi(fibonacci(n)),n=0..35); # Emeric Deutsch
  • Mathematica
    Table[PrimePi[Fibonacci[k+1]]-PrimePi[Fibonacci[k]],{k,50}] (* Vladimir Joseph Stephan Orlovsky, Nov 30 2010 *)
  • PARI
    A076777(n) = primepi(fibonacci(n+1))-primepi(fibonacci(n))
A076777(n) = sum(i=fibonacci(n)+1,fibonacci(n+1),isprime(i)) \\ Michael B. Porter, Nov 24 2009

Formula

a(n) = A000720(A000045(n+1)) - A000720(A000045(n)).

Extensions

More terms from Emeric Deutsch, Mar 02 2005
More terms from Amiram Eldar, Oct 07 2021

A130973 Number of primes between successive pairs of twin primes, for a(n) > 0.

Original entry on oeis.org

1, 1, 2, 1, 4, 3, 4, 2, 1, 3, 1, 2, 3, 10, 4, 7, 4, 3, 2, 1, 2, 18, 2, 2, 17, 1, 2, 6, 9, 3, 1, 1, 1, 8, 3, 2, 15, 1, 4, 1, 1, 7, 7, 4, 4, 3, 4, 1, 1, 7, 2, 5, 1, 5, 18, 2, 5, 4, 3, 1, 5, 1, 18, 12, 2, 8, 1, 4, 2, 5, 4, 1, 1, 1, 9, 10
Offset: 1

Views

Author

Omar E. Pol, Aug 23 2007

Keywords

Comments

a(k) corresponds to the k-th term in the isolated prime sequence A007510 or A134797. a(1) corresponds to 23. a(2) corresponds to 37. a(3) corresponds to 47 and 53. - Enrique Navarrete, Jan 28 2017
Lengths of the runs of consecutive integers in A176656. - R. J. Mathar, Feb 19 2017

Links

Crossrefs

Cf. A001223, A007510 (isolated primes), A027883, A048614, A048198, A052011, A052012, A061273, A076777, A073784, A082602, A088700, A179067 (clusters of twin primes).
Showing 1-2 of 2 results.

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

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