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.

A052012 Number of primes between successive Lucas numbers.

Original entry on oeis.org

1, 0, 1, 0, 2, 2, 4, 6, 9, 15, 20, 31, 48, 72, 110, 170, 257, 400, 608, 950, 1448, 2256, 3487, 5413, 8440, 13118, 20478, 31932, 49995, 78222, 122553, 192262, 301826, 474039, 745772, 1173270, 1848000, 2912623, 4593723, 7249438, 11448047
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1999

Keywords

Examples

			Between L(7)=29 and L(8)=47 we find the following primes: 31, 37, 41 and 43 hence a(7)=4.

Links

Crossrefs

Cf. A000032, A000204, A000720, A001606, A005479, A052011, A277062.

Programs

  • Haskell
    a052012 n = a052012_list !! (n-1)
a052012_list = c 1 0 $ tail a000204_list where
  c x y ls'@(l:ls) | x < l     = c (x+1) (y + a010051 x) ls'
                   | otherwise = y : c (x+1) 0 ls
-- Reinhard Zumkeller, Dec 18 2011
  • Mathematica
    PrimePi[Last[#]-1]-PrimePi[First[#]]&/@Partition[LucasL[ Range[45]],2,1] (* Harvey P. Dale, Jun 28 2011 *)

Formula

a(n) = pi(L(n + 1) - 1) - pi(L(n)), where pi is the prime counting function (A000720) and L = A000032. - Wesley Ivan Hurt, Nov 09 2023
a(n) = A277062(n+1) - A277062(n) - [n+1 in A001606], where [] denotes the Iverson bracket. - Amiram Eldar, Jun 10 2024

A277063 Number of primes <= n-th Bell number.

Original entry on oeis.org

0, 0, 1, 3, 6, 15, 46, 151, 570, 2376, 10961, 54941, 297220, 1720725, 10602541, 69176095, 475881437, 3439093081, 26026621617, 205694058211, 1693554793730, 14494778231067, 128711956613875, 1183763037547762, 11258075170582653, 110558809039675629, 1119649516271861536
Offset: 0

Views

Author

Vincenzo Librandi, Nov 10 2016

Keywords

Links

Crossrefs

Cf. A000110, A000720, A054782, A277062.

Programs

  • Magma
    [#PrimesUpTo(Bell(n)): n in [0..14]];
  • Mathematica
    Table[PrimePi[BellB[n]], {n, 0, 20}]

Formula

a(n) = A000720(A000110(n)). - Michel Marcus, Nov 10 2016

Extensions

a(21)-a(26) from Charles R Greathouse IV, Nov 10 2016

A273974 Number of primes <= n-th Catalan number.

Original entry on oeis.org

0, 0, 1, 3, 6, 13, 32, 82, 226, 651, 1939, 5946, 18637, 59736, 194898, 645742, 2167325, 7359262, 25237989, 87325031, 304549332, 1069685013, 3781189896, 13443608964, 48049822995, 172568075048, 622514907195, 2254799747130, 8197867118026, 29909486953987, 109477635390870
Offset: 0

Views

Author

Vincenzo Librandi, Nov 10 2016

Keywords

Links

Crossrefs

Cf. A000108, A000720, A054782, A277062, A277063.

Programs

  • Magma
    [#PrimesUpTo(Catalan(n)): n in [0..18]];
  • Mathematica
    Table[PrimePi[CatalanNumber[n]], {n, 0, 27}]

Formula

a(n) = A000720(A000108(n)). - Michel Marcus, Nov 10 2016

Extensions

a(28)-a(30) from Amiram Eldar, Sep 03 2024

A274771 Number of primes <= n-th Carmichael lambda number.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 5, 3, 2, 2, 6, 3, 7, 2, 3, 4, 8, 1, 8, 5, 7, 3, 9, 2, 10, 4, 4, 6, 5, 3, 11, 7, 5, 2, 12, 3, 13, 4, 5, 8, 14, 2, 13, 8, 6, 5, 15, 7, 8, 3, 7, 9, 16, 2, 17, 10, 3, 6, 5, 4, 18, 6, 8, 5, 19, 3, 20, 11, 8, 7, 10, 5, 21, 2
Offset: 1

Views

Author

Vincenzo Librandi, Nov 11 2016

Keywords

Crossrefs

Cf. A002322, A054782, A070804, A273974, A277062, A277063.

Programs

  • Magma
    [0] cat [#PrimesUpTo(CarmichaelLambda(n)): n in [2..100]];
  • Maple
    with(numtheory):
a:= n-> pi(lambda(n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 11 2016
  • Mathematica
    Table[PrimePi[CarmichaelLambda[n]], {n, 100}]

Formula

a(n) = A000720(A002322(n)). - Michel Marcus, Nov 11 2016
Showing 1-4 of 4 results.

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