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A306394 Numbers k == 0 or 2 (mod 6) which are not the sum of a prime and the square of a prime. 1

%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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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)