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.

A230285 a(n) = n*prime(prime(n)) - prime(n).

Original entry on oeis.org

1, 7, 28, 61, 144, 233, 396, 517, 724, 1061, 1366, 1847, 2286, 2631, 3118, 3803, 4650, 5033, 6222, 6989, 7634, 8743, 9830, 10975, 12628, 14121, 15098, 16329, 17262, 18397, 21852, 23517, 25372, 26959, 29916, 31421, 33846, 36583, 38482, 41067, 43404, 45473
Offset: 1

Views

Author

V.J. Pohjola, Oct 15 2013

Keywords

Comments

First published at Sequence Fans Mailing List on Oct 12 2013.

Links

Crossrefs

Cf. A000040, A230098.

Programs

  • Mathematica
    Table[n*Prime[Prime[n]] - Prime[n], {n, 1, 100}]
  • PARI
    a(n) = n*prime(prime(n)) - prime(n) \\ Charles R Greathouse IV, Oct 15 2013

Formula

a(n) = A080697(n) - A000040(n). - Omar E. Pol, Oct 21 2013

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)).

A230329 Prime(prime(2*n)) - 2*prime(n).

Original entry on oeis.org

1, 11, 31, 53, 87, 131, 157, 203, 237, 295, 339, 387, 465, 501, 523, 633, 679, 755, 833, 889, 941, 1013, 1051, 1231, 1253, 1297, 1391, 1455, 1523, 1597, 1659, 1801, 1825, 1991, 2053, 2115, 2235, 2321, 2385, 2457, 2551, 2657, 2727, 2843, 2905
Offset: 1

Views

Author

Gerasimov Sergey, Oct 16 2013

Keywords

Comments

For n = 12239, 24046, 24140, 24255, ... a(n+1) = a(n), and for n = 2154, 2524, 2810, 3795, ... a(n+1) < a(n). What is the smallest number n such that a(n+2) <= a(n+1) <= a(n)? - Farideh Firoozbakht, Oct 18 2013
Using the Prime Number Theorem, prime(n) ~ n log n, the asymptotic behavior is the same as that of A217622, a(n) ~ 2n (log 2n) log(2n log 2n). - M. F. Hasler, Oct 19 2013

Crossrefs

Cf. A230098, A230285, A066066.

Programs

  • Mathematica
    Table[Prime[Prime[2n]] - 2Prime[n], {n, 45}]
  • PARI
    A230329(n)=prime(prime(2*n))-2*prime(n) \\ M. F. Hasler, Oct 19 2013

Formula

a(n) = A217622(n) - 2*A000040(n).
a(n) = A217622(n) - A100484(n). - Omar E. Pol, Oct 19 2013

Extensions

Corrected by R. J. Mathar, Oct 18 2013
Showing 1-3 of 3 results.

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