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A116994
Prime partial sums of triangular numbers with prime indices.
2
3, 1759, 3323, 469303, 605113, 641969, 1110587, 1426669, 11148289, 18352349, 20473721, 21820391, 24710753, 30048589, 36690923, 40785301, 97060681, 155135369, 160593239, 168132247, 361391623, 377965069, 416572171, 645803201
OFFSET
1,1
LINKS
FORMULA
A000040 INTERSECTION {A085739 Partial sums of A034953(n)}. Primes in A085739. (Sum_{i=1..k} A000217(A000040(i))) iff in A000040. (Sum_{i=1..k} (A000040(i)*(A000040(i)+1)/2) iff in A000040.
EXAMPLE
a(1) = Sum_{i=1..1} prime(i)*(prime(i)+1)/2 = T(2) = 3.
a(2) = Sum_{i=1..11} prime(i)*(prime(i)+1)/2 = T(2)+T(3)+T(5)+T(7)+T(11)+T(13)+T(17)+T(19)+T(23)+T(29)+T(31) = 1759.
a(3) = Sum_{i=1..13} prime(i)*(prime(i)+1)/2 = 3323.
a(4) = Sum_{i=1..53} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(241) = 469303.
a(5) = Sum_{i=1..57} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(269) = 605113.
a(6) = Sum_{i=1..58} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(271) = 641969.
a(7) = Sum_{i=1..68} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(337) = 1110587.
MAPLE
T:=n->n*(n+1)/2: a:=proc(n): if isprime(sum(T(ithprime(j)), j=1..n))=true then sum(T(ithprime(j)), j=1..n) else fi end: seq(a(n), n=1..500); # Emeric Deutsch, Apr 06 2006
MATHEMATICA
Select[Accumulate[Table[(n(n+1))/2, {n, Prime[Range[500]]}]], PrimeQ] (* Harvey P. Dale, Jan 25 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Apr 02 2006
EXTENSIONS
More terms from Emeric Deutsch, Apr 06 2006
STATUS
approved