A361799 - OEIS

%I #20 May 04 2024 02:47:44

%S 3,7,14,21,23,43,47,62,75,119,134,138,167,215,318,398,566,1487

%N Numbers which cannot be expressed as i^2 + j*k with i >= j >= k >= 0.

%C Is this list infinite?

%C a(19) > 3.5 * 10^8. - _Delbert L. Johnson_, May 04 2024

%H Math Pickle, <a href="https://youtu.be/zhGoDHg1RG0">Big Square Mini Mathematical Universe</a>, YouTube video.

%e 14 is a term because there are no solutions to 14 = i^2 + j*k with i >= j >= k >= 0. Specifically 14 = 3^2 + 5*1 is not a solution because 5 > 3.

%e 117 is not a term because 117 = 9^2 + 6*6.

%e 118 is not a term because 118 = 10^2 + 9*2 (also 118 = 10^2 + 6*3).

%o (PARI) isok(n)={for(k=sqrtint(n\2), sqrtint(n), my(r=n-k^2); if(r==0, return(0)); fordiv(r, d, if(d<=k && r/d<=k, return(0)))); 1}

%o select(isok, [1..2000]) \\ _Andrew Howroyd_, Mar 24 2023

%K nonn,more

%O 1,1

%A _Gordon Hamilton_, Mar 24 2023

%E a(11)-a(18) from _Andrew Howroyd_, Mar 24 2023