OFFSET
1,1
COMMENTS
The following sequences (allowing offset of first term) all appear to have the same parity: A034953, triangular numbers with prime indices; A054269, length of period of continued fraction for sqrt(p), p prime; A082749, difference between the sum of next prime(n) natural numbers and the sum of next n primes; A006254, numbers n such that 2n-1 is prime; A067076, 2n+3 is a prime. - Jeremy Gardiner, Sep 10 2004
Given a rectangular prism with sides 1, p, p^2 for p = n-th prime (n > 1), the area of the six sides divided by the volume gives a remainder which is 4*a(n). - J. M. Bergot, Sep 12 2011
The infinite sum over the reciprocals is given by 2*A179119. - Wolfdieter Lang, Jul 10 2019
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triangular Number.
FORMULA
a(n) = Sum_{k=1..prime(n)} k. - Wesley Ivan Hurt, Apr 27 2021
Product_{n>=1} (1 - 1/a(n)) = A307868. - Amiram Eldar, Nov 07 2022
MAPLE
a:= n-> (p-> p*(p+1)/2)(ithprime(n)):
seq(a(n), n=1..65); # Alois P. Heinz, Apr 20 2022
MATHEMATICA
t[n_] := n(n + 1)/2; Table[t[Prime[n]], {n, 44}] (* Robert G. Wilson v, Aug 12 2004 *)
(#(# + 1))/2&/@Prime[Range[50]] (* Harvey P. Dale, Feb 27 2012 *)
With[{nn=200}, Pick[Accumulate[Range[nn]], Table[If[PrimeQ[n], 1, 0], {n, nn}], 1]] (* Harvey P. Dale, Mar 05 2023 *)
PROG
(PARI) forprime(p=2, 1e3, print1(binomial(p+1, 2)", ")) \\ Charles R Greathouse IV, Jul 19 2011
(PARI) apply(n->binomial(n+1, 2), primes(100)) \\ Charles R Greathouse IV, Jun 04 2013
(Haskell)
a034953 n = a034953_list !! (n-1)
a034953_list = map a000217 a000040_list
-- Reinhard Zumkeller, Sep 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved