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A235716
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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}.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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