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

1, 3, 5, 24, 26, 29, 41, 290, 314, 626, 1784, 6041, 7556, 7589, 8876, 26171, 52454, 153089, 159731, 218084, 576239, 1478531, 2677289, 2934539, 3085781, 3569114, 3802301, 4692866, 24307841, 25051934, 54168539

Offset: 1

Author

Charles R Greathouse IV, Jul 17 2016

Keywords

• nonn

Comments

Position of records in A085099.

On the Bunyakovsky conjecture A085099(n) exists for each n and hence this sequence is infinite since A085099 is unbounded.

Examples

			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:
     1 +   1^2 =     2
     3 +   2^2 =     7
     5 +   6^2 =    41
    24 +   7^2 =    73
    26 +   9^2 =   107
    29 +  12^2 =   173
    41 +  24^2 =   617
   290 +  27^2 =  1019
   314 +  45^2 =  2339
   626 +  69^2 =  5387
  1784 +  93^2 = 10433
  6041 + 114^2 = 19037
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A085099.

Programs

PARI

A085099(n)=my(k); while(!isprime(k++^2+n), ); k
r=0; for(n=1,1e9, t=A085099(n); if(t>r, r=t; print1(n", ")))