A085099 -id:A085099 - 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.

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

Charles R Greathouse IV, Jul 17 2016

nonn

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.

			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

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

Cf. A085099.

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", ")))

A316568 Largest k such that 1^2 + n, 2^2 + n, ..., k^2 + n are composite.

Original entry on oeis.org

0, 0, 1, 0, 5, 0, 1, 2, 1, 0, 5, 0, 1, 2, 1, 0, 5, 0, 1, 2, 3, 0, 5, 6, 1, 8, 1, 0, 11, 0, 3, 2, 1, 2, 5, 0, 1, 2, 1, 0, 23, 0, 1, 2, 3, 0, 5, 4, 1, 2, 3, 0, 5, 4, 1, 8, 1, 0, 17, 0, 5, 2, 1, 2, 5, 0, 1, 8, 1, 0, 5, 0, 3, 2, 1, 4, 5, 0, 1, 2, 3, 0, 11, 4, 1, 8, 3, 0, 11, 6, 3, 2, 1, 2, 5, 0, 1, 2, 1, 0

Offset: 1

Seiichi Manyama, Jul 06 2018

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A085099.

lk[n_]:=Module[{k=1},While[CompositeQ[k^2+n],k++];k-1]; Array[lk,100] (* Harvey P. Dale, Aug 04 2022 *)

a(n) = A085099(n) - 1.

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI