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Search: id:A162869
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| A162869 |
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Primes of the form (x^2+y^3)/(x+y), with x,y >1 two distinct integers. |
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+0
1
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| 3, 7, 13, 31, 43, 67, 73, 109, 139, 149, 157, 179, 193, 211, 229, 241, 307, 317, 379, 389, 421, 457, 463, 491, 499, 593, 601, 647, 661, 751, 757, 769, 829, 839, 937, 1009, 1021, 1033, 1123, 1171, 1213, 1231, 1283, 1319, 1381, 1459, 1481, 1483, 1549, 1621
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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a(1)= 3 = (1^2+2^3)/(1+2). a(2) = 7 = (1^2+3^3)/(1+3) or (6^2+3^3)/(6+3).
a(3) = 13 = (1^2+4^3)/(1+4) or (12^2+4^3)/ (12+4). 31 = (1^2+6^3)/(1+6).
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MAPLE
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isA162869 := proc(p) local a, b ; if isprime(p) then for b from 1 to p do for d in numtheory[divisors](b^2*(b+1)) do a := d-b ; if a > 1 and (a^2+b^3)= p*(a+b) then RETURN(true); fi; od: od: RETURN(false) ; else false; fi; end:
for n from 1 do p := ithprime(n) ; if isA162869(p) then printf("%d, \n", p) ; fi; od: # R. J. Mathar, Sep 22 2009
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MATHEMATICA
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f[a_, b_]:=(a^2+b^3)/(a+b); lst={}; Do[Do[If[f[a, b]==IntegerPart[f[a, b]], If[a!=b&&PrimeQ[f[a, b]], AppendTo[lst, f[a, b]]]], {b, 4*6!}], {a, 4*6!}]; Take[Union[lst], 50]
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CROSSREFS
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Sequence in context: A117708 A093431 A083520 this_sequence A079018 A002383 A163418
Adjacent sequences: A162866 A162867 A162868 this_sequence A162870 A162871 A162872
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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), Jul 15 2009
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EXTENSIONS
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Comment turned into examples - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 22 2009
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