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, 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

Links

Table of n, a(n) for n=1..78.

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

Adjacent sequences: A173750 A173751 A173752 * A173754 A173755 A173756

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Feb 23 2010

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