A096659 Earliest value of C in y = x^2+(2n-1)x+C such that y is prime for all x = 0 to n.

2, 3, 3, 5, 23, 31, 47, 59, 13, 29, 17, 37, 23, 47, 73, 251, 281, 313, 347, 383, 421

Offset: 0

Author

Ray G. Opao, Aug 25 2004

Keywords

• nonn
• more

Comments

a(0) is the first term of A000040; a(1) is the first term of A001359; a(2) is the first term of A046136; a(3) is the first term of A097434; a(4) is the first term of A097436; a(5) is the first term of A097437; a(6) is the first term of A097458; a(7) is the first term of A097459; a(8) is the first term of A097460; a(9) is the first term of A097461.

Sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Aug 11 2013

a(20) > 10^10; probably a(20) > 10^20. - Charles R Greathouse IV, Aug 12 2013

Examples

			Triangle of y, primes, starts:
2,
3, 7,
3, 9, 17,
5, 13, 23, 35,
23, 33, 45, 59, 75,
31, 43, 57, 73, 91, 111,
47, 61, 77, 95, 115, 137, 161,
59, 75, 93, 113, 135, 159, 185, 213,
...
		

Programs

PARI

a(n) = C = 1; ok = 0; while (! ok, ok = 1; for (x = 0, n, if (! isprime(x^2+(2*n-1)*x+C), ok = 0; break;);); if (ok, return (C)); C++;); \\ Michel Marcus, Aug 10 2013

PARI

works(C,n)=for(x=1,n,if(!isprime(x^2+(2*n-1)*x+C), return(0)));1
a(n)=forprime(C=2,,if(works(C,n),return(C))) \\ Charles R Greathouse IV, Aug 12 2013