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A066527
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Triangular numbers that for some k are also the sum of the first k primes.
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13
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(2) = 28, as A000217(7) = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 = 2 + 3 + 5 + 7 + 11 = A007504(5).
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MAPLE
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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)
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a066527 n = a066527_list !! (n-1)
a066527_list = filter ((== 1) . a010054) a007504_list
(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
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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EXTENSIONS
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a(6) from Philip Sung (philip_sung(AT)hotmail.com), Jan 25 2002
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STATUS
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approved
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