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.

A071698 Lesser members of twin prime pairs of form (4*k+3, 4*k+5), k >= 0.

Original entry on oeis.org

3, 11, 59, 71, 107, 179, 191, 227, 239, 311, 347, 419, 431, 599, 659, 827, 1019, 1031, 1091, 1151, 1319, 1427, 1451, 1487, 1607, 1619, 1667, 1787, 1871, 1931, 2027, 2087, 2111, 2267, 2339, 2591, 2687, 2711, 2999, 3119, 3167, 3251, 3299
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 04 2002

Keywords

Comments

Corresponding greater members: A071699(n).

Links

Crossrefs

Cf. A001359, A071695, A071700.
Cf. A010051, subsequence of A004767.

Programs

  • Haskell
    a071698 n = a071698_list !! (n-1)
a071698_list = [x | x <- [3, 7 ..], a010051' x == 1, a010051' (x+2) == 1]
-- Reinhard Zumkeller, Aug 05 2014
  • Magma
    [4*k+3:k in [0..1000]|IsPrime(4*k+3) and IsPrime(4*k+5)]; // Marius A. Burtea, Nov 06 2019
  • Mathematica
    Transpose[Select[Table[4n+{3,5},{n,0,1000}],AllTrue[#,PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 16 2015 *)

Formula

a(n) = 2*A241557(n+1)-1. - Hilko Koning, Nov 06 2019

A071699 Greater members of twin prime pairs of form (4*k+3, 4*k+5), k >= 0.

Original entry on oeis.org

5, 13, 61, 73, 109, 181, 193, 229, 241, 313, 349, 421, 433, 601, 661, 829, 1021, 1033, 1093, 1153, 1321, 1429, 1453, 1489, 1609, 1621, 1669, 1789, 1873, 1933, 2029, 2089, 2113, 2269, 2341, 2593, 2689, 2713, 3001, 3121, 3169, 3253, 3301
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 04 2002

Keywords

Comments

Corresponding lesser members: A071698(n).

Links

Crossrefs

Cf. A071696, A071698, A071700.
Cf. A010051, subsequence of A016813.
Intersection of A006512 and A002144.

Programs

  • Haskell
    a071699 n = a071699_list !! (n-1)
a071699_list = [x | x <- [5, 9 ..], a010051' x == 1, a010051' (x-2) == 1]
-- Reinhard Zumkeller, Aug 05 2014
  • Magma
    [4*(k+1)+1:k in [0..1000]|IsPrime(4*k+3) and IsPrime(4*k+5)]; // Marius A. Burtea, Nov 06 2019
  • Mathematica
    #+2&/@Select[4Range[0,850]+3,PrimeQ[#]&&PrimeQ[#+2]&] (* Harvey P. Dale, Aug 24 2011 *)

Formula

a(n) = 2*A241557(n+1) + 1. - Hilko Koning, Nov 06 2019

A241556 Number of prime anti-divisors m of n.

Original entry on oeis.org

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

Views

Author

Michael De Vlieger, Aug 08 2014

Keywords

Comments

The maximum value of a(n) is 9 for 1 <= n <= 10000.
There are 167 instances of a(n) = 0 for 1 <= n <= 10000 (See A241557).

Examples

			a(10) = 2, since 10 has 3 anti-divisors {3, 4, 7}; only {3, 7} are prime.
a(9223) = 9; these are {2, 3, 5, 7, 11, 13, 17, 31, 43}.

Links

Crossrefs

Cf. A066272, A192281, A242965, A242966, A241557.

Programs

  • Mathematica
    primeAntiDivisors[n_] := Select[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)], PrimeQ]; a241556[n_Integer] := Map[Length[primeAntiDivisors[#]] &, Range[n]]; a241556[120]
Showing 1-3 of 3 results.

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