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Search: id:A145017
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| A145017 |
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Squarefree positive integers n for which n-(floor(sqrt(n)))^2 is a full square |
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+0
3
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| 1, 2, 5, 10, 13, 17, 26, 29, 34, 37, 53, 58, 65, 73, 82, 85, 97, 101, 109, 122, 130, 137, 145, 170, 173, 178, 185, 194, 197, 205, 221, 226, 229, 241, 257, 265, 281, 290, 293, 305
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If an odd prime p divides a(n) then it has the form 4k+1
Conjecture. For every n>=1 there exsist infinitely many primes p of the form 4k+1 for which for a(n)>1 we have sp-(floor(sqrt(sp)))^2 is not a full square for s=1,...,a(n)-1 while a(n)p-(floor(sqrt(a(n)p))^2 is a full square(see A145016(s=1) and A145022, 145023, A145047, A145048, A145149, A145050 correspondingly for s=2, s=5, s=10, s=13, s=17, s=26) [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Sep 30 2008]
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CROSSREFS
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A005117 A020893 A145016
A145016 A145022 A045023 A145047 A145048 A145049 A145050 [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Sep 30 2008]
Sequence in context: A037942 A008784 A020893 this_sequence A003814 A031396 A003654
Adjacent sequences: A145014 A145015 A145016 this_sequence A145018 A145019 A145020
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), Sep 29 2008
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EXTENSIONS
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An additional comment(see below) and new cross-references to other sequences [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Sep 30 2008]
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