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Search: id:A114364
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| A114364 |
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k such that kx^3+x+1 is not prime. |
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+0
1
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| 4, 18, 48, 100, 180, 294, 448, 648, 900, 1210, 1584, 2028, 2548, 3150, 3840, 4624, 5508, 6498, 7600, 8820, 10164, 11638, 13248, 15000, 16900, 18954, 21168, 23548, 26100, 28830, 31744, 34848, 38148, 41650, 45360, 49284, 53428, 57798, 62400
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Theorem: y = kx^3+x+1 is not prime for k = 4,18,48,...,n(n+1)^2. Proof: n(n+1)^2x^3 + x + 1 = ((n+1)x+1)((n^2 + n)x^2 - nx + 1). Thus (n+1)x+1 divides y. This could possibly be used as a pre-test for compositeness. This sequence is the same as beginning with the third term of A045991.
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FORMULA
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k = n(n+1)^2, n=1,2,3,...
a(n)=sum(sum(n, j=2..n),k=1..n): seq(a(n), n>=2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
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MAPLE
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seq(sum ((n+1)^2, k=1..n), n=1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 10 2007
seq(2*binomial(n, 2)*n, n=2..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
a:=n->sum(sum(n, j=2..n), k=1..n): seq(a(n), n=2..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007
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PROGRAM
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(PARI) g2(n) = for(x=1, n, y=x*(x+1)^2; print1(y", "))
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CROSSREFS
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Cf. A045991.
Sequence in context: A023650 A163188 A045991 this_sequence A027271 A073991 A052642
Adjacent sequences: A114361 A114362 A114363 this_sequence A114365 A114366 A114367
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Feb 09 2006
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