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%I #8 Jan 15 2014 08:08:22
%S 180180,270270,300300,330330,390390,420420,540540,660660,840840,
%T 1231230,1261260,1501500,1621620,1861860,1921920,1951950,2012010,
%U 2372370,2762760,2972970,3663660,3693690,3723720,3903900,4084080,4264260,4474470,5135130,5465460,5735730
%N Average of twin prime pairs n having their decimal expansion of the form abcabc or abcabc0 such that n contains three twin primes as divisors.
%C This sequence is an interesting subsequence of A235483 with symmetrical numbers of the form abcabc or abcabc0, and these numbers are divisible by 2*3*5*7*11*13 = 30030. This property of symmetry disappears when length(a(n)) > 7.
%H Michel Lagneau, <a href="/A235716/b235716.txt">Table of n, a(n) for n = 1..44</a>
%e 180180 = 2 ^ 2 * 3 ^ 2 * 5 * 7 * 11 * 13 is in the sequence because the three twin prime divisors are {3,5}, {5,7} and {11, 13}.
%p with(numtheory) :kk:=0:
%p for n from 1 to 10^7 do:
%p p1:=ithprime(n):p2:=ithprime(n+1):
%p if p2=p1+2
%p then
%p ii:=0:x:=factorset(p1+1):n1:=nops(x):
%p for i from 1 to n1-1 do:
%p if x[i+1]=x[i]+2
%p then
%p ii:=ii+1:
%p else fi:
%p od:
%p if ii=3 and irem(p1+1,30030)=0
%p then
%p kk:=kk+1:printf ( "%d %d \n",kk,p1+1):
%p else fi:
%p fi:
%p od:
%Y Cf. A235483.
%K nonn,fini,full
%O 1,1
%A _Michel Lagneau_, Jan 15 2014
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