A122264 a(n) = n + 1 + 2*Sum_{j=0..n-2} (j*prime(n-j+2) - (2*j-1)*prime(n-j+1) + (j-1)*prime(n-j)).

2, 7, 12, 25, 30, 43, 48, 61, 82, 87, 108, 121, 126, 139, 160, 181, 186, 207, 220, 225, 246, 259, 280, 309, 322, 327, 340, 345, 358, 411, 424, 445, 450, 487, 492, 513, 534, 547, 568, 589, 594, 631, 636, 649, 654, 699, 744, 757, 762, 775

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = n + 1 + 2*Sum_{j=0..n-2} (j*prime(n-j+2) - (2*j-1)*prime(n-j+1) + (j-1)*prime(n-j)) with a(1) = 2.

Mathematica

a[n_]:= n+1 +2*Sum[j*Prime[n-j+2] -(2*j-1)*Prime[n-j+1] +(j-1)*Prime[n -j], {j, 0, n-2}];
Table[a[n], {n, 60}] (* G. C. Greubel, Dec 26 2022 *)

Prog

(Magma)
P:=NthPrime;
A122264:= func< n | n eq 1 select 2 else n+1+2*(&+[j*P(n-j+2) -(2*j-1)*P(n-j+1) +(j-1)*P(n-j) : j in [0..n-2]]) >;
[A122264(n): n in [1..60]]; // G. C. Greubel, Dec 26 2022
(SageMath)
p=nth_prime
def A122264(n): return n+1 +2*sum(j*p(n-j+2) -(2*j-1)*p(n-j+1) +(j-1)*p(n-j) for j in range(n-1))
[a122264(n) for n in range(1, 61)] # G. C. Greubel, Dec 26 2022

Crossrefs

Sequence in context: A135541 A288656 A180804 * A379790 A079824 A059329

Adjacent sequences: A122261 A122262 A122263 * A122265 A122266 A122267

Keyword

nonn,easy,less

Author

Roger L. Bagula, Oct 18 2006

Extensions

Edited by G. C. Greubel, Dec 26 2022

Status

approved