A335984 - OEIS

%I #25 May 23 2021 03:24:03

%S 4,5,7,9,11,19,21,31,33,39,49,51,81,99,101,123,129,159,171,177,189,

%T 231,291,441,879,1011,2751

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

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

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

%C There are no more terms below 200000. - _Pontus von Brömssen_, Jul 06 2020

%C Numbers m such that A109909(m) > m/4. - _Pontus von Brömssen_, May 09 2021

%e 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.

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

%p select(filter, [$1..10000]);

%Y Cf. A059036, A109909.

%K nonn,more

%O 1,1

%A _Robert Israel_, Jul 03 2020