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

1,2

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.

Links

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

Example

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

Prog

(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", ")))

Crossrefs

Cf. A085099.

Sequence in context: A050280 A005761 A200948 * A336425 A230985 A286427

Adjacent sequences: A275145 A275146 A275147 * A275149 A275150 A275151

Keyword

nonn

Author

Charles R Greathouse IV, Jul 17 2016

Status

approved