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Search: id:A099332
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| A099332 |
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Primes p such that p = a^2 + b^2 for a,b>0 and a+b is prime. |
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4
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| 2, 5, 13, 17, 29, 37, 61, 73, 89, 97, 101, 109, 149, 157, 181, 193, 229, 241, 257, 269, 277, 293, 349, 409, 421, 433, 461, 521, 541, 593, 601, 641, 661, 701, 709, 733, 769, 797, 829, 853, 881, 929, 937, 953, 997, 1009, 1021, 1049, 1061, 1069, 1109, 1117
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Let q=a+b. For a specific prime q, the number of distinct primes p that are the sum of two squares is A082519(q)/2.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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29 is in this sequence because 29=2^2+5^2 and 2+5 is prime.
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MATHEMATICA
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Needs["NumberTheory`NumberTheoryFunctions`"]; lst={2}; Do[n=4k+1; If[PrimeQ[n], If[PrimeQ[Plus@@QuadraticRepresentation[1, n]], AppendTo[lst, n]]], {k, 500}]; lst
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CROSSREFS
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Cf. A082519 (number of times that k^2 + (n-k)^2 is prime for 1 <= k <= n-1).
Adjacent sequences: A099329 A099330 A099331 this_sequence A099333 A099334 A099335
Sequence in context: A086807 A002313 A068486 this_sequence A031439 A074856 A087952
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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), Oct 15 2004
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