

A268101


Smallest prime p such that some polynomial of the form a*x^2  b*x + p generates distinct primes in absolute value for x = 1 to n, where 0 < a < p and 0 <= b < p.


1



2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 31, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 647, 1277, 1979, 2753
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..44.
Carlos Rivera, Problem 12
Eric Weisstein's World of Mathematics, PrimeGenerating Polynomial


EXAMPLE

a(1) = 2 (a prime), x^2 + 2 gives a prime for x = 1.
a(2) = 3 (a prime), 2*x^2 + 3 gives distinct primes for x = 1 to 2.
a(4) = 5 (a prime), 2*x^2 + 5 gives distinct primes for x = 1 to 4.
a(6) = 7 (a prime), 4*x^2 + 7 gives distinct primes for x = 1 to 6.
a(10) = 11 (a prime), 2*x^2 + 11 gives distinct primes for x = 1 to 10.
a(12) = 13 (a prime), 6*x^2 + 13 gives distinct primes for x = 1 to 12.
a(16) = 17 (a prime), 6*x^2 + 17 gives distinct primes for x = 1 to 16.
a(18) = 19 (a prime), 10*x^2 + 19 gives distinct primes for x = 1 to 18.
a(22) = 23 (a prime), 3*x^2  3*x + 23 gives distinct primes for x = 1 to 22.
a(28) = 29 (a prime), 2*x^2 + 29 gives distinct primes for x = 1 to 28.
a(29) = 31 (a prime), 2*x^2  4*x + 31 gives distinct primes for x = 1 to 29.
a(40) = 41 (a prime), x^2  x + 41 gives distinct primes for x = 1 to 40.
a(41) = 647 (a prime), abs(36*x^2  594*x + 647) gives distinct primes for x = 1 to 41.
a(42) = 1277 (a prime), abs(36*x^2  666*x + 1277) gives distinct primes for x = 1 to 42.
a(43) = 1979 (a prime), abs(36*x^2  738*x + 1979) gives distinct primes for x = 1 to 43.
a(44) = 2753 (a prime), abs(36*x^2  810*x + 2753) gives distinct primes for x = 1 to 44.


CROSSREFS

Cf. A027688, A027753, A027690, A027755, A048058, A048059, A007635, A007639, A007637, A007641, A202018, A005846, A117081, A050268, A268109.
Sequence in context: A113459 A305430 A159477 * A123318 A186698 A234345
Adjacent sequences: A268098 A268099 A268100 * A268102 A268103 A268104


KEYWORD

nonn,hard


AUTHOR

Arkadiusz Wesolowski, Jan 26 2016


STATUS

approved



