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A244066
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Arithmetic mean of two consecutive twin primes that is also the arithmetic mean of two consecutive non-twin primes.
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1
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30, 42, 60, 105, 144, 165, 192, 228, 270, 312, 462, 570, 600, 858, 870, 882, 1026, 1092, 1230, 1254, 1290, 1302, 1428, 1482, 1620, 1878, 1998, 2028, 2340, 2550, 2688, 2730, 2760, 3345, 3540, 3582, 3627, 3795, 3885, 4020, 4338, 4500, 4518, 4650, 4755, 4788, 4866
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OFFSET
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1,1
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COMMENTS
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Intersection of A162734 (averages of consecutive non-twin primes) and A163656 (averages of consecutive twin primes).
a(n)/3 are: 10, 14, 20, 35, 48, ...
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LINKS
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EXAMPLE
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30 is in this sequence because it is the arithmetic mean of 29 and 31, consecutive terms of A001097, as well as of 23 and 37, consecutive terms of A007510.
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MATHEMATICA
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Module[{prs=Prime[Range[800]], tp, nt}, tp=Flatten[Select[Partition[ prs, 2, 1], #[[2]]- #[[1]]==2&]]; nt=Complement[prs, tp]; Select[Tally[ Join[ Mean/@ Partition[tp, 2, 1], Mean/@Partition[nt, 2, 1]]], #[[2]]==2&][[All, 1]]] (* Harvey P. Dale, Sep 03 2016 *)
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PROG
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(PARI)
a244066(pmax) = {
my(tp=[], m, j, k, s=[]);
forprime(p=2, pmax, if(isprime(p-2) || isprime(p+2), tp=concat(tp, p)));
for(i=1, #tp-1,
m=(tp[i]+tp[i+1])\2;
j=1; while(!(isprime(m+j) && !isprime(m+j-2) && !isprime(m+j+2)), j++);
k=1; while(!(isprime(m-k) && !isprime(m-k-2) && !isprime(m-k+2)), k++);
if(j==k, s=concat(s, m))
);
s
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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