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A096659 Earliest value of C in y = x^2+(2n-1)x+C such that y is prime for all x = 0 to n. 0
2, 3, 3, 5, 23, 31, 47, 59, 13, 29, 17, 37, 23, 47, 73, 251, 281, 313, 347, 383, 421 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

LINKS

Table of n, a(n) for n=0..20.

EXAMPLE

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,

...

PROG

(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

CROSSREFS

Sequence in context: A263769 A064776 A270592 * A154695 A154646 A046826

Adjacent sequences:  A096656 A096657 A096658 * A096660 A096661 A096662

KEYWORD

nonn,more

AUTHOR

Ray G. Opao, Aug 25 2004

STATUS

approved

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Last modified August 12 16:40 EDT 2020. Contains 336439 sequences. (Running on oeis4.)