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A143766
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a(n+1) = a(n)^2 + 3*n*a(n) + n^2, a(1) = 1.
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6
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1, 5, 59, 4021, 16216709, 262981894041341, 69159476593575838635509822455, 4783033202697364284917104840982811414253511628131328498629, 22877406618105405861781317490149379589769149890660405723416585348109182559037843469373513563751798569651299138846801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Let f(n+1,k) = f(n,k)^2 + k*n*f(n,k) + n^2, f(1, k) = 1:
f(n,0)=A143760(n), f(n,-1)=A143761(n), f(n,+1)=A143762(n),
f(n,-2)=A143763(n), f(n,+2)=A143764(n), f(n,-3)=A143765(n), f(n,+3)=a(n).
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LINKS
| Index entries for sequences of form a(n+1)=a(n)^2 + ... [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 11 2008]
Dario A. Alpern, Factorization using the Elliptic Curve Method [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 11 2008]
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EXAMPLE
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 11 2008: (Start)
a(4)=A000040(556);
a(5)=19*199*4289;
a(6)=3686299*71340359;
a(7)=5*89*23581*36190079671*182112572569;
A055642(a(8))=58; A001221(a(8))=A001222(a(8))=3;
A055642(A020639(a(8)))=4, A020639(a(8))=2459;
A055642(A006530(a(8)))=43, A006530(a(8))=1145781805709434583439407716589323093429591;
A055642(a(9))=116; A001221(a(9))=A001222(a(9))=3;
A055642(A020639(a(9)))=5, A020639(a(9))=52291;
A055642(A087039(a(9)))=39, A087039(a(9))=823717865733493312451872329574156137131;
A055642(A006530(a(9)))=72, A006530(a(9))=531130643259166452223939782963931943654770628199012648274446497807560081;
factorizations made with Dario Alpern's ECM applet. (End)
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CROSSREFS
| Sequence in context: A093946 A001059 A120608 * A132549 A091457 A100906
Adjacent sequences: A143763 A143764 A143765 * A143767 A143768 A143769
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 01 2008
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