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.
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
Offset: 1
Examples
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.
Links
- Carlos Rivera, Problem 12
- Eric Weisstein's World of Mathematics, Prime-Generating Polynomial