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A188269
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Prime numbers of the form k^4 + k^3 + 4*k^2 + 7*k + 5 = k^4 + (k+1)^3 + (k+2)^2.
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1
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59, 348077, 10023053, 30414227, 55367063, 72452489, 85856933, 109346759, 182679473, 254112143, 305966369, 433051637, 727914497, 2029672529, 4178961167, 6528621257, 8346080159, 12783893813, 17220494579, 17993776223, 19618171127, 23673478589, 29448235247, 43333033853
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OFFSET
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1,1
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COMMENTS
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All the terms in the sequence are congruent to 2 mod 3. - K. D. Bajpai, Apr 11 2014
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LINKS
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EXAMPLE
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5 is prime and appears in the sequence because 0^4 + 1^3 + 2^2 = 5.
59 is prime and appears in the sequence because 2^4 + 3^3 + 4^2 = 59.
348077 = 24^4 + (24+1)^3 + (24+2)^2 = 24^4 + 25^3 + 26^2.
10023053 = 56^4 + (56+1)^3 + (56+2)^2 = 56^4 + 57^3 + 58^2.
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MAPLE
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%p KD := proc(n) local a, b, d; a:=(n)^4+(n+1)^3+(n+2)^2; if isprime(a) then RETURN (a); fi; end: seq(KD(n), n=0..1000); # K. D. Bajpai, Apr 11 2014
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MATHEMATICA
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lst={}; Do[If[PrimeQ[p=n^4+n^3+4*n^2+7*n+5], AppendTo[lst, p]], {n, 200}]; lst
Select[Table[n^4+n^3+4n^2+7n+5, {n, 500}], PrimeQ] (* Harvey P. Dale, Jun 19 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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