cp's OEIS Frontend

A275148 Numbers m where the least natural number k such that m + k^2 is prime reaches a new record value.

%I A275148 #14 Jan 01 2024 13:30:32
%S A275148 1,3,5,24,26,29,41,290,314,626,1784,6041,7556,7589,8876,26171,52454,
%T A275148 153089,159731,218084,576239,1478531,2677289,2934539,3085781,3569114,
%U A275148 3802301,4692866,24307841,25051934,54168539
%N A275148 Numbers m where the least natural number k such that m + k^2 is prime reaches a new record value.
%C A275148 Position of records in A085099.
%C A275148 On the Bunyakovsky conjecture A085099(n) exists for each n and hence this sequence is infinite since A085099 is unbounded.
%H A275148 Charles R Greathouse IV, <a href="/A275148/b275148.txt">Table of n, a(n) for n = 1..40</a>
%e A275148 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 A275148      1 +   1^2 =     2
%e A275148      3 +   2^2 =     7
%e A275148      5 +   6^2 =    41
%e A275148     24 +   7^2 =    73
%e A275148     26 +   9^2 =   107
%e A275148     29 +  12^2 =   173
%e A275148     41 +  24^2 =   617
%e A275148    290 +  27^2 =  1019
%e A275148    314 +  45^2 =  2339
%e A275148    626 +  69^2 =  5387
%e A275148   1784 +  93^2 = 10433
%e A275148   6041 + 114^2 = 19037
%o A275148 (PARI) A085099(n)=my(k); while(!isprime(k++^2+n), ); k
%o A275148 r=0; for(n=1,1e9, t=A085099(n); if(t>r, r=t; print1(n", ")))
%Y A275148 Cf. A085099.
%K A275148 nonn
%O A275148 1,2
%A A275148 _Charles R Greathouse IV_, Jul 17 2016