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%I #14 Jan 01 2024 13:30:32
%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 m where the least natural number k such that m + k^2 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 as follows:
%e 1 + 1^2 = 2
%e 3 + 2^2 = 7
%e 5 + 6^2 = 41
%e 24 + 7^2 = 73
%e 26 + 9^2 = 107
%e 29 + 12^2 = 173
%e 41 + 24^2 = 617
%e 290 + 27^2 = 1019
%e 314 + 45^2 = 2339
%e 626 + 69^2 = 5387
%e 1784 + 93^2 = 10433
%e 6041 + 114^2 = 19037
%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", ")))
%Y Cf. A085099.
%K nonn
%O 1,2
%A _Charles R Greathouse IV_, Jul 17 2016
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