

A275148


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


2



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

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


LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



