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Numbers k such that there is no prime of the form 2k + p^2 for any prime p.
10

%I #16 May 17 2024 09:55:57

%S 13,28,34,43,55,58,67,73,76,88,97,100,103,106,118,133,139,145,148,157,

%T 160,163,166,178,181,184,193,199,202,208,214,223,232,238,244,253,259,

%U 262,265,268,271,283,286,298,301,307,310,313,328,331,340,343,349,352

%N Numbers k such that there is no prime of the form 2k + p^2 for any prime p.

%C Indices where zero occurs in A138479.

%C For primes in this sequences see A138686.

%H Alois P. Heinz, <a href="/A138685/b138685.txt">Table of n, a(n) for n = 1..10000</a>

%F Based on comments from _Zak Seidov_, _Don Reble_ and _M. F. Hasler_, we now know that these are the numbers k such that k == 1 (mod 3) and 2k + 9 is composite. - _N. J. A. Sloane_, Apr 20 2008

%t a = {}; Do[p = 0; While[(! PrimeQ[2*n + Prime[p + 1]^2]) && (p < 10000), p++ ]; If[p < 10000,[null], AppendTo[a, n]], {n, 1, 550}]; a

%t Select[Range[400],Mod[#,3]==1&&CompositeQ[2#+9]&] (* _Harvey P. Dale_, Feb 23 2017 *)

%Y Cf. A138479, A138686.

%K nonn

%O 1,1

%A _Artur Jasinski_, Mar 26 2008