A378493 Dot product of the first n primes and the first n triangular numbers.

2, 11, 41, 111, 276, 549, 1025, 1709, 2744, 4339, 6385, 9271, 13002, 17517, 23157, 30365, 39392, 49823, 62553, 77463, 94326, 114313, 137221, 163921, 195446, 230897, 269831, 313273, 360688, 413233, 476225, 545393, 622250, 704955, 798825, 899391, 1009762

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Formula

a(n) mod 2 = A166486(n-1).

Example

a(3) = dot product of {2,3,5} and {1,3,6} = 2*1+3*3+5*6 = 41.

Maple

a:= proc(n) option remember; `if`(n<1, 0,
      a(n-1)+ithprime(n)*n*(n+1)/2)
    end:
seq(a(n), n=1..37);  # Alois P. Heinz, Nov 28 2024

Mathematica

Table[Prime[Range[n]].Accumulate[Range[n]], {n, 50}]

Crossrefs

Partial sums of A196421.

Cf. A000040, A000217, A166486.

Sequence in context: A066593 A173580 A062256 * A024522 A144841 A203245

Adjacent sequences: A378490 A378491 A378492 * A378494 A378495 A378496

Keyword

nonn

Author

Harvey P. Dale, Nov 28 2024

Status

approved