

A275148


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


1



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
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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:
1 + 1^2
3 + 2^2
5 + 6^2
24 + 7^2
26 + 9^2
29 + 12^2
41 + 24^2
290 + 27^2
314 + 45^2
626 + 69^2
1784 + 93^2
6041 + 114^2


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

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



