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A116994
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Prime partial sums of triangular numbers with prime indices.
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1
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3, 1759, 3323, 469303, 605113, 641969, 1110587, 1426669, 11148289, 18352349, 20473721, 21820391, 24710753, 30048589, 36690923, 40785301, 97060681, 155135369, 160593239, 168132247, 361391623, 377965069, 416572171, 645803201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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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
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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 (deutsch(AT)duke.poly.edu), Apr 06 2006
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CROSSREFS
| Cf. A000040, A000217, A034953, A085739.
Sequence in context: A060307 A119111 A118050 * A172940 A096730 A193149
Adjacent sequences: A116991 A116992 A116993 * A116995 A116996 A116997
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 02 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006
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