A066886 Sum of the elements in any transversal of a prime(n) X prime(n) array containing the numbers from 1 to prime(n)^2 in standard order.

5, 15, 65, 175, 671, 1105, 2465, 3439, 6095, 12209, 14911, 25345, 34481, 39775, 51935, 74465, 102719, 113521, 150415, 178991, 194545, 246559, 285935, 352529, 456385, 515201, 546415, 612575, 647569, 721505, 1024255, 1124111, 1285745

Offset

1,1

Comments

a(n) is the sum of the primes in a prime(n) X prime(n) example of Haga's conjecture (see link below).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Carlos Rivera, The prime puzzles & problems connection, conjecture 26, The Prime Puzzles and Problems Connection.

Formula

a(n) = prime(n)*(prime(n)^2+1)/2, where prime(n) is the n-th prime.

a(n) = A006003(prime(n)). - Michel Marcus, Apr 04 2018

a(n) = A006254(n-1)^4 - A005097(n-1)^4, for n>1. - Dimitris Valianatos, Apr 10 2018

Maple

map(t -> t*(t^2+1)/2, [seq(ithprime(i), i=1..100)]); # Robert Israel, Apr 04 2018

Mathematica

a[n_] := Prime[n] (Prime[n]^2 + 1)/2; Table[a[n], {n, 50}]

Prog

(PARI) apply(x->(x*(x^2+1)/2), primes(100)) \\ Michel Marcus, Apr 04 2018

Crossrefs

Cf. A005097, A006003, A006254, A066883, A066885.

Sequence in context: A149615 A149616 A189945 * A149617 A149618 A323793

Adjacent sequences: A066883 A066884 A066885 * A066887 A066888 A066889

Keyword

easy,nonn

Author

Enoch Haga, Jan 22 2002

Extensions

Edited by Dean Hickerson, Jun 08 2002

Status

approved