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%I #9 Jan 26 2014 15:20:22
%S 6,12,18,24,30,36,42,60,66,72,90,102,108,138,144,150,174,180,192,198,
%T 228,240,270,276,282,294,312,348,354,384,420,426,432,462,522,540,570,
%U 600,618,624,642,660,666,696,714,756,780,810,822,828,858,864,882,930
%N Multiples of 6 that either are Averages of Twin Prime Pairs (ATPP), or become ATPP when multiplied by 3.
%C The first 10k terms of this sequence are 45.37% pseudo ATPP, and are about 9.71% of all multiples of 6 up to 617694. All numbers in this sequence that end 4 or 6 are ATPP/3 (but the reverse is not true).
%H Michael G. Kaarhus, <a href="/A236240/b236240.txt">Table of n, a(n) for n = 1..10000</a>
%e 660 is in this sequence because it is an ATPP. 666 is in this sequence because 666 * 3 = 1998 is an ATPP.
%o (Maxima) load(basic)$ a:[]$ p:-1$ j:0$ m:0$
%o chli():= block (if w>341550071728321 then
%o (n:11000, print("# over limit") ), return)$
%o for n:1 thru 10000 step 0 do
%o (p:p+6, q:p+1, r:p+2, if (primep(p) and primep(r)) then
%o (push(q, a), n:n+1, j:j+1) else
%o (w:3*q, chli(), if (primep(w-1) and primep(w+1)) then
%o (push(q, a), n:n+1, m:m+1
%o ) ) )$
%o a:reverse(a)$ d:length(a)$ k:float(m*100/d)$ h:", "$
%o y:last(a)$ b:float(d*100/(y/6))$
%o print("# Real ATPP = ", j, h, " Pseudo ATPP = ", m, h, " Percent pseudo = ", k)$
%o print("# First ", d, " of sequence are ", b, "% of ints. up to ", y, " cong. to 0 mod 6.")$ for i:1 thru d do (s:pop(a), print(i, h, s) )$
%Y Subsequence of A008588 (Multiples of 6)
%K nonn
%O 1,1
%A _Michael G. Kaarhus_, Jan 20 2014
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