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

1,1

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).

Links

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

Example

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

Prog

(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) )$

Crossrefs

Subsequence of A008588 (Multiples of 6)

Sequence in context: A078596 A187389 A085129 * A242650 A083263 A194385

Adjacent sequences: A236237 A236238 A236239 * A236241 A236242 A236243

Keyword

nonn

Author

Michael G. Kaarhus, Jan 20 2014

Status

approved