OFFSET
1,1
COMMENTS
These are the 4, 7, 516, 2904, 328777, ... -th triangular numbers and are the sums of the first 3, 5, 217, 1065, 93448, ... prime numbers respectively.
a(7) is the sum of the first 240439822 primes. a(8) is the sum of the first 1894541497 primes. - Donovan Johnson, Nov 24 2008
a(9) is the sum of the first 132563927578 primes. a(10) is the sum of the first 309101198255 primes. a(11) > 6640510710493148698166596 (sum of first pi(2*10^13) primes). - Donovan Johnson, Aug 23 2010
EXAMPLE
MAPLE
a066527(m) = local(d, ds, p, ps); d=1; ds=1; p=2; ps=2; while(ds<m, if(ds==ps, print1(ds, ", "); d++; ds=ds+d; p++; p=nextprime(p); ps=ps+p, if(ds<ps, d++; ds=ds+d, p++; p=nextprime(p); ps=ps+p))) a066527(10^11)
MATHEMATICA
s = 0; Do[s = s + Prime[n]; t = Floor[ Sqrt[2*s]]; If[t*(t + 1) == 2s, Print[s]], {n, 1, 10^6} ]
Select[Accumulate[Prime[Range[5000000]]], IntegerQ[(Sqrt[1+8#]-1)/2]&] (* Harvey P. Dale, May 04 2013 *)
PROG
(Haskell)
a066527 n = a066527_list !! (n-1)
a066527_list = filter ((== 1) . a010054) a007504_list
-- Reinhard Zumkeller, Mar 23 2013
(Python)
from sympy import integer_nthroot, isprime, nextprime
def istri(n): return integer_nthroot(8*n+1, 2)[1]
def afind(limit):
s, p = 2, 2
while s < limit:
if istri(s): print(s, end=", ")
p = nextprime(p)
s += p
afind(10**11) # Michael S. Branicky, Oct 28 2021
CROSSREFS
KEYWORD
nonn,nice,more
AUTHOR
Reinhard Zumkeller, Jan 06 2002
EXTENSIONS
a(5) from Klaus Brockhaus and Robert G. Wilson v, Jan 07 2002
a(6) from Philip Sung (philip_sung(AT)hotmail.com), Jan 25 2002
a(7)-a(8) from Donovan Johnson, Nov 24 2008
a(9)-a(10) from Donovan Johnson, Aug 23 2010
STATUS
approved