A235716 - OEIS

%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