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.

A217622 Prime(prime(2*n)).

Original entry on oeis.org

5, 17, 41, 67, 109, 157, 191, 241, 283, 353, 401, 461, 547, 587, 617, 739, 797, 877, 967, 1031, 1087, 1171, 1217, 1409, 1447, 1499, 1597, 1669, 1741, 1823, 1913, 2063, 2099, 2269, 2351, 2417, 2549, 2647, 2719, 2803, 2909, 3019, 3109, 3229, 3299, 3407, 3517
Offset: 1

Views

Author

Vincenzo Librandi, Oct 13 2012

Keywords

Comments

Subsequence of A006450.
Using the Prime Number Theorem, prime(n) ~ n log n, the asymptotic behavior is A217622(n) ~ 2n (log 2n) log(2n log 2n) ~ 2n (log n)^2 ~ A230460(n). - M. F. Hasler, Oct 19 2013

Links

Crossrefs

Cf. A000040, A006450, A066066, A031215, A230460.

Programs

  • Magma
    [NthPrime(NthPrime(2*n)): n in [1..50] ]; //
  • Mathematica
    Table[Prime[Prime[2n]], {n, 100}]
  • PARI
    a(n)=prime(prime(2*n)) \\ Charles R Greathouse IV, Oct 20 2013

Formula

a(n) = A000040(A031215(n)). - Omar E. Pol, Oct 19 2013
a(n) = A006450(2n). - M. F. Hasler, Oct 20 2013

A230481 a(n) = prime(prime(2*n)) - prime(2*prime(n)).

Original entry on oeis.org

-2, 4, 12, 24, 30, 56, 52, 78, 84, 82, 108, 88, 126, 144, 126, 162, 150, 204, 210, 210, 248, 242, 234, 348, 266, 268, 320, 362, 380, 394, 304, 396, 340, 480, 378, 420, 466, 486, 476, 464, 498, 578, 476, 566, 592, 678, 600, 456, 524, 660, 714, 742, 768, 756
Offset: 1

Views

Author

M. F. Hasler, Oct 20 2013

Keywords

Comments

As difference of two odd primes, all terms are even.

Links

Crossrefs

Cf. A066066, A000040, A006450, A031215, A217622, A230460.

Programs

  • PARI
    a=n->prime(prime(2*n))-prime(2*prime(n))

Formula

a(n) = A217622(n) - A230460(n) = 2*A230482(n).

A230482 a(n) = (prime(prime(2*n)) - prime(2*prime(n)))/2.

Original entry on oeis.org

-1, 2, 6, 12, 15, 28, 26, 39, 42, 41, 54, 44, 63, 72, 63, 81, 75, 102, 105, 105, 124, 121, 117, 174, 133, 134, 160, 181, 190, 197, 152, 198, 170, 240, 189, 210, 233, 243, 238, 232, 249, 289, 238, 283, 296, 339, 300, 228, 262, 330, 357, 371, 384, 378, 372
Offset: 1

Views

Author

M. F. Hasler, Oct 20 2013

Keywords

Comments

As difference of two odd primes, all terms of A230481(n) = prime(prime(2*n))-prime(2*prime(n)) are even, which motivates to define the present sequence.
Further values: a(100)=617, a(10^3)=9344, a(10^4)=114171, a(10^5)=1325772, a(10^6)=14979156; a(10^10)~2.2*10^11, a(10^20)~3.9*10^21, a(10^30)~5.5*10^31.

Links

Crossrefs

Cf. A066066, A000040, A006450, A031215, A217622, A230460.

Programs

  • PARI
    a=n->(prime(prime(2*n))-prime(2*prime(n)))/2

Formula

a(n) = (A217622(n) - A230460(n))/2.

A228529 a(n) = prime(n*prime(n)).

Original entry on oeis.org

3, 13, 47, 107, 257, 397, 653, 881, 1279, 1889, 2293, 3119, 3847, 4423, 5323, 6563, 7937, 8819, 10391, 11833, 12889, 14831, 16477, 18713, 21599, 23603, 25189, 27409, 29063, 31511, 37159, 39869, 43321, 45589, 50923, 53281, 57271, 61561, 65173, 69821, 74383
Offset: 1

Views

Author

Omar E. Pol, Oct 20 2013

Keywords

Examples

			For n = 2, prime(2*prime(2)) = prime(2*3) = prime(6) = 13, so a(2) = 13.

Crossrefs

Cf. A000040, A006450, A033286, A036689, A080697, A217622, A230098, A230325, A230285, A230460.

Programs

  • Mathematica
    Table[Prime[n*Prime[n]], {n, 100}] (* T. D. Noe, Oct 22 2013 *)
  • PARI
    a(n) = prime(n*prime(n)); \\ Michel Marcus, Oct 22 2013

Formula

a(n) = A000040(A033286(n)).
Showing 1-4 of 4 results.

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