|
%I #15 Dec 27 2016 23:12:30
%S 0,0,1,0,1,1,1,1,1,0,1,2,2,1,1,1,2,2,3,2,3,3,2,1,2,2,2,2,1,1,2,2,3,3,
%T 2,2,3,2,3,3,1,4,3,1,4,3,2,3,4,3,2,5,3,2,4,2,4,4,3,4,4,3,3,5,2,2,6,4,
%U 2,5,4,3,6,3,2,3,4,4,5,3,2,6,4,3,5,1,5,6,2,3,4,4,3,6,3,4,8,3,3,4,3,3,5,2,2,6,4,3,6,5
%N Number of primes of the form 4(n - k - 1) + 3 where 0 <= k and prime of the form 4k + 3 <= n.
%C (1) Conjecture: a(n) > 0 for n >= 11.
%C (2) Conjecture: A278287(n) > 0 for n >= 11.
%C Conjecture (1) and conjecture (2) are first and second parts of Goldbach-like conjecture in A001031.
%e a(12) = 2 because 4*(12-0-1)+3 = 47 and 4*0+3 = 3 are primes where 3 < 12 and 4*(12-1-1)+3 = 43 and 4*1+3 = 7 are primes where 7 < 12.
%Y Cf. A001031, A002144, A278287.
%K nonn
%O 1,12
%A _Juri-Stepan Gerasimov_, Dec 26 2016
|
