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.

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

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