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A173753
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.
0
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
OFFSET
1,5
EXAMPLE
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).
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Cf. A007635.
Sequence in context: A335616 A004596 A118653 * A295753 A144968 A239328
KEYWORD
nonn,less
AUTHOR
EXTENSIONS
a(31) and a(33) corrected and sequence extended by R. J. Mathar, Mar 01 2010
Name edited by Jon E. Schoenfield, Jan 30 2019
STATUS
approved