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Search: id:A116911
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| A116911 |
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Prime partial sums of pentagonal numbers with prime indices. |
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1
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| 5, 17, 4957, 129277, 2826443, 3861083, 5126483, 9451573, 19811083, 53751743, 68136617, 98729003, 264616831, 388771421, 498157871, 608312141, 682548511, 779346653, 918754301, 1174179079, 1700023891, 2056298683, 2149703411
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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See also: A116994 Prime partial sums of triangular numbers with prime indices. A116995 Pentagonal numbers with prime indices.
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FORMULA
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A000040 INTERSECTION {Partial sums of A116995(n)}. (SUM[i=1..k] A000326(A000040(i))) iff in A000040. (SUM[i=1..k] (Prime(i)*(3*Prime(i)-1)/2) iff in A000040.
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EXAMPLE
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a(1) = SUM[i=1..1] (Prime(i)*(3*Prime(i)-1)/2) = P(2) = 5.
a(2) = SUM[i=1..2] (Prime(i)*(3*Prime(i)-1)/2) = P(2)+P(3) = 17.
a(3) = SUM[i=1..11] (Prime(i)*(3*Prime(i)-1)/2) = P(2)+P(3)+P(5)+P(7)+P(11)+P(13)+P(17)+P(19)+P(23)+P(29)+P(31) = 4957.
a(4) = P(2)+...+P(103) = 129277.
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MAPLE
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P:=n->n*(3*n-1)/2: seq(P(n), n=0..10): a:=proc(n) if isprime(sum(P(ithprime(j)), j=1..n))=true then sum(P(ithprime(j)), j=1..n) else fi end: seq(a(n), n=1..600); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 15 2006
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CROSSREFS
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Cf. A000040, A000217, A034953, A085739, A116994, A116995.
Sequence in context: A119531 A085832 A062223 this_sequence A097491 A120087 A022142
Adjacent sequences: A116908 A116909 A116910 this_sequence A116912 A116913 A116914
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 03 2006
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 15 2006
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