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.

A109724 Sum of the first n^2 primes.

Original entry on oeis.org

0, 2, 17, 100, 381, 1060, 2427, 4888, 8893, 15116, 24133, 36888, 54169, 77136, 106733, 144526, 191755, 249748, 320705, 406048, 507825, 627294, 768373, 931686, 1119887, 1336090, 1583293, 1864190, 2180741, 2536646, 2935471, 3380980
Offset: 0

Views

Author

Giovanni Teofilatto, Aug 10 2005

Keywords

Comments

Partial sums of A109725.
a(n) = A007504(n^2).
a(n) = A109724(n) is prime for a(1) = 2, a(2) = 17, a(8) = 8893, a(10) = 24133, a(22) = 68373, a(26) = 1583293, a(28) = 2180741. a(n) is semiprime for a(4) = 381 = 3 * 127, a(6) = 2427 = 3 * 809, a(12) = 54169 = 19 * 2851, a(16) = 191755 = 5 * 38351, a(24) = 1119887 = 89 * 12583. a(n) is square for a(3) = 100. These subsequences might be worth extending. - Jonathan Vos Post, Aug 13 2005
Prime a(n) are listed in A122207[n] = {2,17,8893,24133,768373,1583293,2180741,3875933,6426919,173472547,289093219,741938801,2738357903,2895147163,3058653607,...}. Numbers n such that a(n) is a prime are listed in A122208[n] = {1,2,8,10,22,26,28,32,36,78,88,110,150,152,154,...}. - Alexander Adamchuk, Aug 25 2006

Links

  • Ray Chandler, Table of n, a(n) for n = 0..10000 (first 500 terms from Vincenzo Librandi) [It was suggested that the initial terms of this b-file were wrong, but in fact they are correct. - _N. J. A. Sloane_, Jan 19 2019]

Crossrefs

Cf. A007504, A109722-A109726, A122207, A122208.

Programs

  • Mathematica
    f[n_] := Sum[Prime[k], {k, n}]; Table[f[n^2], {n, 0, 32}]
  • PARI
    a(n)=vecsum(primes(n^2)) \\ Charles R Greathouse IV, Sep 15 2015

Formula

a(n) ~ n^4 log n. - Charles R Greathouse IV, Sep 15 2015 (Corrected by N. J. A. Sloane, Jan 19 2019)

Extensions

Edited and extended by Ray Chandler, Aug 11 2005

A122208 Numbers n such that the sum of the first n^2 primes A109724(n) = A007504(n^2) is a prime.

Original entry on oeis.org

1, 2, 8, 10, 22, 26, 28, 32, 36, 78, 88, 110, 150, 152, 154, 232, 252, 258, 264, 316, 320, 324, 368, 376, 426, 496, 516, 532, 608, 644, 666, 686, 764, 828, 832, 880, 932, 958, 1020, 1090, 1096, 1106, 1122, 1156, 1174, 1206, 1264, 1280, 1282, 1290, 1296, 1326
Offset: 1

Views

Author

Alexander Adamchuk, Aug 25 2006

Keywords

Comments

Corresponding primes that are equal to the sum of the first a(n)^2 primes are listed in A122207(n) = {2, 17, 8893, 24133, 768373, 1583293, 2180741, 3875933, 6426919, 173472547, 289093219, 741938801, 2738357903, 2895147163, 3058653607, ...}. - Robert G. Wilson v, Sep 29 2006

Links

Crossrefs

Cf. A122207, A109724, A007504.

Programs

  • Mathematica
    s = 0; t = {}; Do[s = s + Sum[Prime@k, {k, (n - 1)^2 + 1, n^2}]; If[PrimeQ@s, AppendTo[t, n]], {n, 1341}]; t (* Robert G. Wilson v *)

Formula

A122207(n) = A109724( a(n) ) = A007504( a(n)^2 ). - Robert G. Wilson v, Sep 29 2006

Extensions

More terms from Robert G. Wilson v, Sep 29 2006

A322420 Sum of the first n*(n+1) primes.

Original entry on oeis.org

0, 5, 41, 197, 639, 1593, 3447, 6601, 11599, 19113, 29897, 44683, 64615, 90763, 124211, 166551, 218759, 283081, 360979, 454095, 564319, 694297, 846287, 1021511, 1223095, 1454367, 1717867, 2016457, 2352313, 2728929, 3149913, 3619807, 4141547
Offset: 0

Views

Author

Ray Chandler, Dec 07 2018

Keywords

Comments

Partial sums of A109726.

Links

Crossrefs

Cf. A002378, A007504, A109722-A109726, A122207, A122208, A322421, A322422.

Programs

  • Mathematica
    f[n_] := Sum[Prime[k], {k, n}]; Table[f[n*(n+1)], {n, 0, 32}]
Module[{nn=40,ap},ap=Join[{0},Accumulate[Prime[Range[nn^2-nn+1]]]];Table[ ap[[n^2-n+1]],{n,nn}]] (* Harvey P. Dale, Jul 14 2021 *)

Formula

a(n) = A007504(A002378(n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.