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Search: id:A077773
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| A077773 |
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Number of integers between n^2 and (n+1)^2 that are the sum of two squares; multiple representations are counted once. |
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+0
3
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| 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 6, 9, 8, 8, 10, 10, 11, 11, 12, 11, 14, 12, 13, 15, 16, 15, 15, 17, 16, 17, 19, 18, 19, 20, 19, 20, 21, 20, 22, 22, 24, 22, 25, 23, 26, 26, 24, 29, 26, 27, 28, 27, 29, 26, 31, 32, 30, 29, 33, 33, 31, 31, 35, 34, 35, 35, 35, 36, 37, 37, 33, 42, 37, 38
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Related to the circle problem, cf. A077770. See A077774 for a more restrictive case. A077768 counts the representations multiply.
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EXAMPLE
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a(8)=6 because 65=64+1=49+16, 68=64+4, 72=36+36, 73=64+9, 74=49+25 and 80=64+16 are between squares 64 and 81. Note that 65 is counted only once.
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MATHEMATICA
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maxN=100; lst={}; For[n=1, n<=maxN, n++, sqrs={}; i=n; j=0; While[i>=j, j=1; While[i^2+j^2<(n+1)^2, If[i>=j&&i^2+j^2>n^2, AppendTo[sqrs, i^2+j^2]]; j++ ]; i--; j-- ]; AppendTo[lst, Length[Union[sqrs]]]]; lst
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CROSSREFS
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Cf. A077768, A077770, A077774.
Sequence in context: A089792 A081608 A096532 this_sequence A076370 A112318 A078489
Adjacent sequences: A077770 A077771 A077772 this_sequence A077774 A077775 A077776
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 20 2002
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