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A235716 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. 2
180180, 270270, 300300, 330330, 390390, 420420, 540540, 660660, 840840, 1231230, 1261260, 1501500, 1621620, 1861860, 1921920, 1951950, 2012010, 2372370, 2762760, 2972970, 3663660, 3693690, 3723720, 3903900, 4084080, 4264260, 4474470, 5135130, 5465460, 5735730 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..44

EXAMPLE

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}.

MAPLE

with(numtheory) :kk:=0:

     for n from 1 to 10^7 do:

         p1:=ithprime(n):p2:=ithprime(n+1):

           if p2=p1+2

           then

           ii:=0:x:=factorset(p1+1):n1:=nops(x):

        for i from 1 to n1-1 do:

           if x[i+1]=x[i]+2

           then

           ii:=ii+1:

           else fi:

        od:

           if ii=3 and irem(p1+1, 30030)=0

           then

           kk:=kk+1:printf ( "%d %d \n", kk, p1+1):

           else fi:

           fi:

       od:

CROSSREFS

Cf. A235483.

Sequence in context: A204787 A060232 A190380 * A274365 A209828 A133541

Adjacent sequences:  A235713 A235714 A235715 * A235717 A235718 A235719

KEYWORD

nonn,fini,full

AUTHOR

Michel Lagneau, Jan 15 2014

STATUS

approved

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Last modified May 8 15:54 EDT 2021. Contains 343666 sequences. (Running on oeis4.)