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Search: id:A134002
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| A134002 |
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Positive integers n such that n(n+5)=a(a+5)+b(b+5) is solvable in positive integers. |
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+0
2
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| 5, 10, 11, 13, 15, 16, 20, 23, 24, 25, 30, 31, 33, 35, 36, 37, 38, 40, 42, 45, 46, 47, 49, 50, 55, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 75, 76, 80, 81, 84, 85, 86, 88, 89, 90, 92, 95, 98, 99, 100, 101, 102, 105, 108, 110, 111, 112, 114, 115, 118, 120, 124, 125
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture. If n a positive integer not a term of this sequence, then n^2+(n+5)^2 is prime. (This has been verified up to n=500.) Examples. For n=1,2,3,4,6,7, n^2+(n+5)^2 is 37, 53,73, 97, 157, and 193, each of which is prime. See A134003 for the complement of this sequence.
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EXAMPLE
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5(5+5)=50=14+36=2(2+5)+4(4+5), so 5 is a term of the sequence.
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CROSSREFS
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Cf. A012132, A027861, A134003.
Sequence in context: A032242 A107975 A106792 this_sequence A028760 A028807 A070791
Adjacent sequences: A133999 A134000 A134001 this_sequence A134003 A134004 A134005
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Oct 01 2007
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