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.

A137291 Numbers m such that prime(m)^2-2 is prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 10, 12, 14, 15, 18, 20, 24, 27, 28, 31, 32, 34, 40, 43, 47, 48, 51, 52, 55, 62, 65, 68, 72, 82, 86, 87, 91, 94, 99, 100, 104, 107, 111, 119, 123, 128, 129, 130, 132, 133, 134, 135, 139, 141, 150, 152, 170, 172, 177, 180, 182, 191, 200, 202, 209, 211
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 05 2008

Keywords

Comments

For m>=1, for these and only these numbers m, A242719(m) = prime(m)^2 + 1. Since A242719(m) >= prime(m)^2 + 1, then the equality is obtained on this and only this sequence. - Vladimir Shevelev, Sep 04 2014

Examples

			prime(24)*prime(24)-2 = 89*89-2 = 7919 is prime, so n=24 belongs to the sequence.

Links

Crossrefs

Cf. A000040, A062326, A242719, A242720, A246824, A010051, A049001, A103960, A210481.

Programs

  • Haskell
    a137291 n = a137291_list !! (n-1)
a137291_list = filter ((== 1) . a010051' . a049001) [1..]
-- Reinhard Zumkeller, Jul 30 2015
  • Mathematica
    Select[Range[211],PrimeQ[Prime[#]^2-2]&] (* James C. McMahon, May 28 2025 *)
  • PARI
    is(n,p=prime(n))=isprime(p^2-2) \\ Charles R Greathouse IV, Feb 17 2017

Formula

A103960(a(n)) - A210481(a(n)) = 1. - Reinhard Zumkeller, Jul 30 2015
a(n) = A049084(A049002(n)). - R. J. Mathar, Apr 09 2008

Extensions

More terms from R. J. Mathar, Apr 09 2008
Offset corrected by Reinhard Zumkeller, Jul 30 2015

A210481 Given n-th prime p, a(n) = number of primes of the form p * q - 2 where q is any prime < p.

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 1, 1, 4, 2, 2, 4, 3, 2, 4, 3, 4, 3, 4, 4, 6, 3, 4, 5, 3, 5, 5, 4, 3, 6, 4, 7, 5, 4, 6, 5, 7, 9, 7, 5, 6, 5, 6, 6, 8, 5, 7, 9, 5, 6, 7, 5, 7, 7, 9, 10, 3, 11, 8, 11, 6, 9, 8, 12, 8, 9, 7, 10, 9, 7, 8, 8, 6, 14, 8, 10, 11, 11, 12, 11, 7, 7
Offset: 1

Views

Author

Jayanta Basu, Apr 18 2013

Keywords

Comments

Very similar to A103960. - T. D. Noe, Apr 18 2013
a(A137291(n)) = A103960(A137291(n)) - 1. - Reinhard Zumkeller, Jul 30 2015

Links

Crossrefs

Cf. A103960, A224748.
Cf. A010051, A000040, A103960, A137291.

Programs

  • Haskell
    a210481 n = sum [a010051' $ p * q - 2 |
                 let p = a000040 n, q <- takeWhile (< p) a000040_list]
-- Reinhard Zumkeller, Jul 30 2015
  • Mathematica
    Table[p = Prime[n]; c = 0; Do[If[PrimeQ[p*Prime[i] - 2], c = c + 1], {i, n - 1}]; c, {n, 82}]
Table[With[{pr=Prime[Range[n]]},Count[Most[pr]Last[pr]-2,?PrimeQ]],{n,90}] (* _Harvey P. Dale, Jul 19 2020 *)

A224961 a(n) = number of primes of the form p * q + 2 where p is the prime(n) and q is any prime < p.

Original entry on oeis.org

0, 0, 1, 2, 1, 2, 2, 3, 3, 2, 1, 4, 0, 4, 4, 4, 5, 4, 4, 3, 2, 4, 4, 3, 5, 3, 4, 4, 6, 4, 7, 4, 4, 7, 5, 5, 6, 5, 6, 8, 5, 7, 7, 6, 3, 9, 5, 8, 5, 8, 7, 10, 9, 7, 8, 8, 5, 8, 8, 9, 8, 8, 10, 7, 11, 13, 8, 10, 10, 10, 11, 9, 12, 9, 13, 11, 9, 12, 7, 11
Offset: 1

Views

Author

Jayanta Basu, Apr 21 2013

Keywords

Examples

			For n=4, p=7, there are a(4)=2 solutions from 7*3+2=23 and 7*5+2=37.

Crossrefs

Cf. A103960, A224748, A210481.

Programs

  • Mathematica
    Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p*Prime[i] + 2], c = c + 1]; i++]; c, {n, 80}]
Table[Count[Prime[n]Prime[Range[n-1]]+2,?PrimeQ],{n,80}] (* _Harvey P. Dale, Feb 28 2023 *)
Showing 1-3 of 3 results.

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