

A236240


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


1



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
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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(w1) 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



