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A328298 The smaller prime in the decomposition of 2n (>=6) into a sum of two odd primes obtained from increasing the smaller prime of such a decomposition of 2n-2.

%I A328298 #10 Oct 09 2020 10:51:50
%S A328298 3,3,5,5,7,5,7,7,11,11,13,11,13,13,17,17,19,17,19,13,17,19,19,23,23,
%T A328298 19,29,29,31,23,29,31,29,31,37,29,31,37,41,41,43,41,43,31,41,43,37,41,
%U A328298 43,43,47,47,43,53,53,43,47,53,61,53,59,61,59,61,67,53,59
%N A328298 The smaller prime in the decomposition of 2n (>=6) into a sum of two odd primes obtained from increasing the smaller prime of such a decomposition of 2n-2.
%C A328298 This sequence is different from A002374 from the 23rd term on.
%e A328298 For the 3rd even number 6, 6=3+3;
%e A328298 For the 4th number 8, increasing the first prime in 6=3+3 by 2, we get 8=5+3, 5 and 3 are both primes, choose the smaller one, the second term of this sequence is 3, which makes 8=3+5;
%e A328298 ...
%e A328298 For the 23rd even number 46, increasing the first prime in 44=13+31 by 2, we get 46=15+31.  15 is not prime, keep increasing: 46=17+29.  Both 17 and 29 are primes, so the 23rd term of this sequence is 17, as of 46=17+29;
%e A328298 ...
%e A328298 For 28th even number 56, increasing the first prime in 54=23+31 by 2, we get 56=25+31.  25 is not prime, keep increasing, 56 = 27+29 = 29+27 = 31+25 = 33+23 = 35+21 = 37+19.  Both 37 and 19 are primes, and 19 is smaller.  So the 28th term of this sequence is 19, as of 56=19+37.
%t A328298 e = 4; p1 = 1; p2 = 3; a = Table[e = e + 2; If[p1 < p2, p1 = p1 + 2, p2 = p2 + 2];
%t A328298   While[! (PrimeQ[p1] && PrimeQ[p2]), p1 = p1 + 2; p2 = p2 - 2];
%t A328298   If[p1 > p2, p1 = p2; p2 = e - p1]; p1, {i, 1, 67}]
%Y A328298 Cf. A002374, A112823.
%K A328298 easy,nonn
%O A328298 3,1
%A A328298 _Lei Zhou_, Oct 11 2019