

A258661


Positive integers m such that none of the four consecutive numbers m, m+1, m+2, m+3 can be written as p^2 + q with p and q both prime.


1



1, 2, 1009, 3598, 4354, 9214, 11662, 15051, 15052, 15873, 15874, 19042, 21772, 22497, 22498, 24334, 26242, 46654, 60514, 76173, 76174, 93634, 97341, 97342, 108898, 112893, 112894, 121101, 121102, 133954, 152098, 156813, 156814, 166462, 171393, 171394, 181473, 181474, 202498, 213441, 213442, 224674, 236193, 236194, 254013, 254014, 266253, 266254, 272482, 278781
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OFFSET

1,2


COMMENTS

Conjecture: Any term not among 1, 2, 1009, 15051, 15052, 21772 has the form 36*k^22 or the form 36*k^23, where k is a positive integer.
Note that this conjecture implies the conjecture in A258168 since neither 36*k^22 nor 36*k^23 can be a multiple of 5.
For more comments, see the linked message to Number Theory Mailing List.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..500
ZhiWei Sun, Re: A new conjecture involving p^2+q, a message to Number Theory Mailing List, May 30, 2015.


EXAMPLE

a(1) = 1 since none of 1,2,3,4 has the form p^2+q with p and q both prime.
a(2) = 2 since none of 2,3,4,5 has the form p^2+q with p and q both prime.


MATHEMATICA

n=0; Do[Do[If[PrimeQ[m+rPrime[k]^2], Goto[aa]], {r, 0, 3}, {k, 1, PrimePi[Sqrt[m+r]]}]; n=n+1; Print[n, " ", m]; Label[aa]; Continue, {m, 1, 278781}]


CROSSREFS

Cf. A000040, A258139, A258140, A258141, A258168.
Sequence in context: A190579 A271527 A214543 * A024033 A255569 A004897
Adjacent sequences: A258658 A258659 A258660 * A258662 A258663 A258664


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Jun 06 2015


STATUS

approved



