A275148 - OEIS

%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