%I
%S 1,3,5,24,26,29,41,290,314,626,1784,6041,7556,7589,8876,26171,52454,
%T 153089,159731,218084,576239,1478531,2677289,2934539,3085781,3569114,
%U 3802301,4692866,24307841,25051934,54168539
%N Numbers n where the least natural number k such that k^2 + n is prime reaches a new record value.
%C Position of records in A085099.
%C On the Bunyakovsky conjecture A085099(n) exists for each n and hence this sequence is infinite since A085099 is unbounded.
%H Charles R Greathouse IV, <a href="/A275148/b275148.txt">Table of n, a(n) for n = 1..40</a>
%e 26 + 9^2 is prime, and 26 + 1^2, 26 + 2^2, ..., 26 + 8^2 are all composite; numbers 1..25 all have some square less than 9^2 for which the sum is prime, so 26 is in this sequence. The first few primes generated by these terms are:
%e 1 + 1^2
%e 3 + 2^2
%e 5 + 6^2
%e 24 + 7^2
%e 26 + 9^2
%e 29 + 12^2
%e 41 + 24^2
%e 290 + 27^2
%e 314 + 45^2
%e 626 + 69^2
%e 1784 + 93^2
%e 6041 + 114^2
%o (PARI) A085099(n)=my(k); while(!isprime(k++^2+n), ); k
%o r=0; for(n=1,1e9, t=A085099(n); if(t>r, r=t; print1(n", ")))
%K nonn
%O 1,2
%A _Charles R Greathouse IV_, Jul 17 2016
