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A050796
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Numbers n such that n^2 + 1 is expressible as the sum of two nonzero squares in at least one way (the trivial solution n^2+1 = n^2+1^2 does not count).
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4
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1, 7, 8, 12, 13, 17, 18, 21, 22, 23, 27, 28, 30, 31, 32, 33, 34, 37, 38, 41, 42, 43, 44, 46, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 64, 67, 68, 70, 72, 73, 75, 76, 77, 78, 80, 81, 82, 83, 86, 87, 88, 89, 91, 92, 93, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 107
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Analogous solutions exist for the sum of two identical squares z^2+1 = 2.r^2 (e.g. 41^2+1 = 2.29^2). Values of 'z' are the terms in sequence A002315, values of 'r' are the terms in sequence A001653.
Apart from the first term, numbers n such that (n^2)! ==0 mod (n^2+1)^2. -Michel Lagneau, Feb 14 2012.
Numbers n such that neither n^2 + 1 nor (n^2 + 1)/2 are prime. [Charles R Greathouse IV, Feb 14 2012]
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LINKS
| Index entries for sequences related to sums of squares
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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EXAMPLE
| E.g. 57^2 + 1 = 15^2 + 55^2 = 21^2 + 53^2 = 35^2 + 45^2.
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PROG
| (PARI) is(n)=!isprime((n^2+1)/if(n%2, 2, 1)) \\ Charles R Greathouse IV, Feb 14 2012
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CROSSREFS
| Cf. A050795, A050798, A002315, A001653, A000129.
Sequence in context: A117619 A098731 A105740 * A106630 A050798 A057484
Adjacent sequences: A050793 A050794 A050795 * A050797 A050798 A050799
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KEYWORD
| nonn,changed
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Sep 15 1999.
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