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.

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

A109722 Sum of first 2n primes.

Original entry on oeis.org

0, 5, 17, 41, 77, 129, 197, 281, 381, 501, 639, 791, 963, 1161, 1371, 1593, 1851, 2127, 2427, 2747, 3087, 3447, 3831, 4227, 4661, 5117, 5589, 6081, 6601, 7141, 7699, 8275, 8893, 9523, 10191, 10887, 11599, 12339, 13101, 13887, 14697, 15537, 16401, 17283
Offset: 0

Views

Author

Giovanni Teofilatto, Aug 10 2005

Keywords

Comments

Bisection of A007504.

Links

Crossrefs

Cf. A007504, A109723, A109724, A109725, A109726.

Programs

  • Mathematica
    f[n_] := Sum[Prime[k], {k, n}]; Table[f[2n], {n, 0, 43}]
Join[{0},With[{nn=100},Take[Accumulate[Prime[Range[nn]]],{2,nn,2}]]] (* Harvey P. Dale, Dec 20 2021 *)

Formula

a(n) = A007504(2n).

Extensions

Edited and extended by Ray Chandler, Aug 11 2005

A109726 Divide primes in groups with 2n elements and add together.

Original entry on oeis.org

0, 5, 36, 156, 442, 954, 1854, 3154, 4998, 7514, 10784, 14786, 19932, 26148, 33448, 42340, 52208, 64322, 77898, 93116, 110224, 129978, 151990, 175224, 201584, 231272, 263500, 298590, 335856, 376616, 420984, 469894, 521740, 577304, 634990
Offset: 0

Views

Author

Giovanni Teofilatto, Aug 10 2005

Keywords

Comments

First difference of A322420.

Links

Crossrefs

Cf. A007504, A109722-A109725, A322420.

Programs

  • Mathematica
    f[n_] := Sum[Prime[k], {k, n}]; Table[f[n*(n + 1)] - f[n*(n - 1)], {n, 0, 34}]

Formula

a(n) = A007504(n*(n+1)) - A007504(n*(n-1)).

Extensions

Edited and extended by Ray Chandler, Aug 11 2005

A109723 Sum of the first 2n+1 primes.

Original entry on oeis.org

2, 10, 28, 58, 100, 160, 238, 328, 440, 568, 712, 874, 1060, 1264, 1480, 1720, 1988, 2276, 2584, 2914, 3266, 3638, 4028, 4438, 4888, 5350, 5830, 6338, 6870, 7418, 7982, 8582, 9206, 9854, 10538, 11240, 11966, 12718, 13490, 14288, 15116, 15968, 16840
Offset: 0

Views

Author

Giovanni Teofilatto, Aug 10 2005

Keywords

Comments

Bisection of A007504.

Links

Crossrefs

Cf. A007504, A109722, A109724, A109725, A109726.

Programs

  • Mathematica
    f[n_] := Sum[Prime[k], {k, n}]; Table[f[2n + 1], {n, 0, 42}]
Take[Accumulate[Prime[Range[160]]], {1,160,2}] (* Harvey P. Dale, Jan 11 2011 *)
  • PARI
    a(n) = sum(k=1, 2*n+1, prime(k)); \\ Michel Marcus, Jan 31 2019

Formula

a(n) = A007504(2n+1).

Extensions

Edited and extended by Ray Chandler, Aug 11 2005
Showing 1-4 of 4 results.

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