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Search: id:A161665
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| A161665 |
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Primes that can be represented as a sum of 2 and also as a sum of 3 distinct nonzero squares, sharing a term in the sums. |
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1
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| 29, 101, 109, 149, 173, 181, 229, 233, 241, 269, 293, 389, 401, 409, 421, 433, 449, 521, 569, 641, 661, 677, 701, 757, 761, 769, 797, 821, 857, 877, 881, 941, 1021, 1069, 1097, 1109, 1117, 1181, 1229, 1237, 1277, 1289, 1301, 1373, 1381, 1429, 1433, 1481, 1549
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Dropping the requirement of one shared term, we would get the super-sequence 17, 29, 41, 53, 61, 73... [R. J. Mathar, Oct 04 2009]
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EXAMPLE
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The prime 29 has the representations 29 = 2^2+ 5^2 = 2^2+3^2+4^2, sharing 2^2.
The prime 101 has the representations 101 = 1^2+10^2 = 1^2+6^2+8^2, sharing 1^2.
The prime 109 has the representations 109 = 3^2+10^2 = 3^2+6^2+8^2, sharing 3^2.
The prime 149 has the representations 149 = 7^2+10^2 = 6^2+7^2+8^2, sharing 7^2.
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MATHEMATICA
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f[n_]:=Module[{k=1}, While[(n-k^2)^(1/2)!=IntegerPart[(n-k^2)^(1/2)], k++; If[2*k^2>=n, k=0; Break[]]]; k]; lst={}; Do[a=f[n]; If[a>0, b=f[n-(f[n])^2]; If[b>0, c=(n-a^2-b^2)^(1/2); If[a!=b&&a!=c, If[PrimeQ[n], AppendTo[lst, n]]]]], {n, 3, 4*6!}]; lst
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CROSSREFS
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Cf. A002114, A085317.
Sequence in context: A154405 A092373 A087641 this_sequence A127464 A142109 A069472
Adjacent sequences: A161662 A161663 A161664 this_sequence A161666 A161667 A161668
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009
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EXTENSIONS
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Definition reverse-engineered from program by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 04 2009
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