A335984 Numbers m such that more than half the distinct positive terms of the sequence -k^2 + m*k - 1 are primes.

4, 5, 7, 9, 11, 19, 21, 31, 33, 39, 49, 51, 81, 99, 101, 123, 129, 159, 171, 177, 189, 231, 291, 441, 879, 1011, 2751

Offset: 1

Author

Robert Israel, Jul 03 2020

Keywords

• nonn
• more

Comments

Numbers m such that more than half the distinct terms in row m-2 of the triangular array A059036 are prime.

All positive terms of the sequence are prime for m = 1, 2, 4, 5, 9 and 21.

There are no more terms below 200000. - Pontus von Brömssen, Jul 06 2020

Numbers m such that A109909(m) > m/4. - Pontus von Brömssen, May 09 2021

Examples

			7 is in the sequence because with g(k) = -k^2+7*k-1, the positive terms of the sequence g(k) are 5=g(1), 9=g(2) and 11=g(3), and two out of the three (5 and 9) are prime.
		

Crossrefs

Cf. A059036, A109909.

Programs

Maple

filter:= n -> nops(select(isprime, [seq(n*x-x^2-1,x=1..n/2)])) > 1/2*floor(n/2):
select(filter, [$1..10000]);