A236240 Multiples of 6 that either are Averages of Twin Prime Pairs (ATPP), or become ATPP when multiplied by 3.

6, 12, 18, 24, 30, 36, 42, 60, 66, 72, 90, 102, 108, 138, 144, 150, 174, 180, 192, 198, 228, 240, 270, 276, 282, 294, 312, 348, 354, 384, 420, 426, 432, 462, 522, 540, 570, 600, 618, 624, 642, 660, 666, 696, 714, 756, 780, 810, 822, 828, 858, 864, 882, 930

Offset: 1

Author

Michael G. Kaarhus, Jan 20 2014

Keywords

• nonn

Comments

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).

Examples

			660 is in this sequence because it is an ATPP.  666 is in this sequence because 666 * 3 = 1998 is an ATPP.
		

Links

• Michael G. Kaarhus, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A008588 (Multiples of 6)

Programs

Maxima

load(basic)$ a:[]$ p:-1$ j:0$ m:0$
chli():= block (if w>341550071728321 then
   (n:11000, print("# over limit") ), return)$
for n:1 thru 10000 step 0 do
   (p:p+6, q:p+1, r:p+2, if (primep(p) and primep(r)) then
      (push(q, a), n:n+1, j:j+1) else
         (w:3*q, chli(), if (primep(w-1) and primep(w+1)) then
            (push(q, a), n:n+1, m:m+1
   )     )  )$
a:reverse(a)$ d:length(a)$ k:float(m*100/d)$ h:", "$
y:last(a)$ b:float(d*100/(y/6))$
print("# Real ATPP = ", j, h, " Pseudo ATPP = ", m, h, " Percent pseudo = ", k)$
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) )$