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A173753
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Let f(j) = j^2 + j + 17 and g(j) = j^2 - j + 17. Sequence gives pi(f(j)) - pi(g(j)) as j runs through those nonnegative integers for which both f(j) and g(j) are prime.
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0
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0, 1, 1, 1, 2, 3, 2, 4, 3, 4, 3, 4, 5, 6, 3, 6, 6, 7, 5, 9, 9, 8, 9, 7, 8, 15, 13, 12, 11, 14, 16, 14, 16, 17, 20, 19, 23, 17, 20, 26, 22, 27, 30, 23, 25, 28, 26, 32, 36, 26, 35, 25, 30, 31, 33, 34, 33, 40, 41, 36, 39, 43, 36, 40, 41, 49, 43, 48, 47, 51, 55, 53, 47, 58, 54, 56, 63, 60
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OFFSET
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1,5
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LINKS
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EXAMPLE
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a(1) = 7 - 7 = 0 where 0^2 + 0 + 17 = 17 = prime(7) and 0^2 - 0 + 17 = 17 = prime(7);
a(2) = 8 - 7 = 1 where 1^2 + 1 + 17 = 19 = prime(8) and 1^2 - 1 + 17 = 17 = prime(7);
a(3) = 9 - 8 = 1 where 2^2 + 2 + 17 = 23 = prime(9) and 2^2 - 2 + 17 = 19 = prime(8);
a(4) = 10 - 9 = 1 where 3^2 + 3 + 17 = 29 = prime(10) and 3^2 - 3 + 17 = 23 = prime(9).
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MAPLE
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for x from 0 to 1000 do mp := x^2+x+17 ; kp := x^2-x+17 ; if isprime(mp) and isprime(kp) then m := numtheory[pi](mp) ; k := numtheory[pi](kp) ; printf("%d, ", m-k) ; end if; end do : # R. J. Mathar, Mar 01 2010
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MATHEMATICA
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f[n_]:=Module[{c=n^2+17, a, b}, a=c+n; b=c-n; If[And@@PrimeQ[{a, b}], PrimePi[a]- PrimePi[b], 0]]; Join[{0}, Select[Array[f, 400, 0], #!=0&]] (* Harvey P. Dale, Jul 13 2011 *)
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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EXTENSIONS
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a(31) and a(33) corrected and sequence extended by R. J. Mathar, Mar 01 2010
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STATUS
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approved
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