A344411 Sum of the prime numbers in the interval (2n, 3n].

3, 5, 7, 11, 24, 30, 36, 59, 42, 52, 83, 60, 97, 138, 152, 168, 168, 221, 184, 243, 263, 220, 287, 311, 384, 384, 410, 493, 493, 523, 462, 462, 559, 593, 696, 732, 768, 881, 881, 802, 802, 719, 846, 977, 888, 1025, 1164, 1164, 1067, 1216, 1266, 1163, 1320, 1213, 1267, 1434

Offset

1,1

Comments

For n >= 3, a(n) is the sum of the prime numbers appearing in the 3rd row of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = Sum_{k=2*n+1..3*n} k * (pi(k) - pi(k-1)).

Example

                                                      [1   2  3  4  5  6]
                                   [1   2  3  4  5]   [7   8  9 10 11 12]
                   [1   2  3  4]   [6   7  8  9 10]   [13 14 15 16 17 18]
         [1 2 3]   [5   6  7  8]   [11 12 13 14 15]   [19 20 21 22 23 24]
         [4 5 6]   [9  10 11 12]   [16 17 18 19 20]   [25 26 27 28 29 30]
         [7 8 9]   [13 14 15 16]   [21 22 23 24 25]   [31 32 33 34 35 36]
----------------------------------------------------------------------------
  n         3            4                5                    6
----------------------------------------------------------------------------
  a(n)      7           11               24                   30
----------------------------------------------------------------------------

Mathematica

Table[Sum[k*(PrimePi[k] - PrimePi[k - 1]), {k, 2 n + 1, 3 n}], {n, 80}]

Crossrefs

Cf. A000720 (pi), A108954.

Sequence in context: A226017 A303705 A309520 * A265687 A023368 A295973

Adjacent sequences: A344408 A344409 A344410 * A344412 A344413 A344414

Keyword

nonn

Author

Wesley Ivan Hurt, May 17 2021

Status

approved