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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..44.

Carlos Rivera, Problem 12

Eric Weisstein's World of Mathematics, Prime-Generating 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

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Last modified May 14 09:14 EDT 2021. Contains 343879 sequences. (Running on oeis4.)