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A162930
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Primes that can be written as a sum of a positive square and a positive cube in more than one way.
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1
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17, 89, 233, 449, 577, 593, 1289, 1367, 1601, 1753, 2089, 2521, 3391, 4481, 4721, 5953, 6121, 6427, 7057, 7577, 8081, 9649, 10313, 10657, 10729, 11969, 12329, 13121, 13457, 15137, 15193, 15641, 15661, 16033, 16649, 18523, 21673, 21961, 23201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A subset of these, 2089, 4481, 7057, 15193, 15641 etc, allows this representation in more than two ways.
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FORMULA
| A000040 INTERSECT A054402.
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EXAMPLE
| The prime 17 can be written 1^3+4^2 as well as 2^3+3^2.
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MAPLE
| isA162930 := proc(n) if isprime(n) then wa := 0 ; for y from 1 to n/2 do if issqr(n-y^3) then if n -y^3 > 0 then wa := wa+1 ; fi; fi; od: RETURN( wa>1) ; else false; fi; end:
for i from 1 to 2700 do if isA162930 ( ithprime(i)) then printf("%d, ", ithprime(i)) ; fi; od: # R. J. Mathar, Jul 21 2009
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MATHEMATICA
| lst={}; Do[Do[AppendTo[lst, n^2+m^3], {n, 2*5!}], {m, 2*5!}]; lst=Sort[lst]; lst2={}; Do[If[lst[[n]]==lst[[n+1]]&&PrimeQ[lst[[n]]], AppendTo[lst2, lst[[n]]]], {n, Length[lst]-1}]; lst2;
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CROSSREFS
| Cf. A054402, A123364
Sequence in context: A061679 A033654 A139947 * A138338 A200670 A057638
Adjacent sequences: A162927 A162928 A162929 * A162931 A162932 A162933
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 17 2009
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EXTENSIONS
| Slightly edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 21 2009
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