%I #16 Feb 12 2019 14:22:33
%S 0,2,8,18,24,74,170,324,614,704,1010,1164,1296,2304,3600,4356,5184,
%T 6084,9216,10404,11664,14400,15054,15876,19044,20736,21774,22500,
%U 24336,24476,26244,28224,34596,39204,41616,44100,46656,49284,51984,60516,66564,69696,72900,76176,82944,90000,93636,97344
%N Numbers k == 0 or 2 (mod 6) which are not the sum of a prime and the square of a prime.
%C Contains 36*k^2 unless 6*k-1 is in A005384.
%C Are 2, 8, 18, 24, 74, 170, 614, 704, 1010, 1164, 15054, 21774, 24476 the only terms not == 0 or 36 (mod 144)?
%H Robert Israel, <a href="/A306394/b306394.txt">Table of n, a(n) for n = 1..652</a>
%H A. V. Kumchev and J. Y. Liu, <a href="https://doi.org/10.1007/s00605-008-0047-1">Sums of primes and squares of primes in short intervals</a>, Monatsh. Math. 157 (2009), 335-363.
%e 24 is in the sequence because 24 == 0 (mod 6) and 24 can't be written as p+q^2 where p and q are primes.
%p N:= 50000: # to get all terms <= N
%p P:= select(isprime,[2,seq(i,i=3..N,2)]):
%p P2:= select(`<=`,map(`^`,P,2),N):
%p PP2:= {seq(seq(s+t,s=P),t=P2)}:
%p sort(convert({seq(seq(6*i+j,i=1=0..(N-j)/6),j=[0,2])} minus PP2,list));
%Y Cf. A005384, A109136.
%K nonn
%O 1,2
%A _Robert Israel_, Feb 12 2019
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