A345469 - OEIS

%I #5 Jun 20 2021 11:08:13

%S 1,2,12,6,14,30,111,74,117,198,89,336,174,116,489,264,101,1251,2730,

%T 308,3219,4836,1274,2466,3999,1130,7266,15571,440,3225,4989,866,4674,

%U 8916,1154,22395,24786,1226,30126,26439,3110,26781,27366,3191,4149,12729,446,54759,26946,3779,16044,26841,4301

%N a(n) is the least k such that A345468(k) = 2*n-1.

%C a(n) is the least k such that (2*n-1)^2+4*k is prime but (2*m-1)^2+4*k is composite for all m from 1 to n-1.

%e a(4) = 6 because 2*4-1 = 7 and 7^2+4*6 = 73 is prime but 1^2+4*6 = 25, 3^2+4*6 = 33 and 5^2+4*6=49 are not.

%p f:= proc(n) local k,m;

%p   m:= 4*n;

%p   for k from 1 by 2 do

%p     if isprime(k^2+m) then return k fi

%p   od

%p end proc:

%p V:= Vector(119):

%p count:= 0:

%p for n from 1 while count < 60 do

%p   v:= f(n);

%p   if v <= 119 and V[v]=0 then V[v]:= n; count:= count+1 fi

%p od:

%p seq(V[2*i-1],i=1..60);

%Y Cf. A345468.

%K nonn

%O 1,2

%A _Robert Israel_, Jun 20 2021