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A294075
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a(n) is the distance from the n-th isolated prime number to the average of the next twin prime pair.
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0
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2, 7, 5, 13, 7, 5, 23, 19, 13, 5, 25, 11, 7, 23, 17, 13, 7, 17, 5, 7, 19, 13, 7, 5, 19, 5, 31, 17, 11, 67, 61, 53, 47, 41, 37, 31, 23, 19, 11, 23, 19, 13, 5, 55, 43, 35, 31, 23, 19, 13, 29, 23, 13, 7, 23, 13, 7, 11, 5, 11, 13, 7, 137, 133
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OFFSET
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1,1
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LINKS
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EXAMPLE
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For n=2, the second isolated prime number is 23. The next twin prime pair after 23 is (29, 31). The average (29 + 31)/2 = 30. The difference 30 - 23 = 7 is the second term.
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MATHEMATICA
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Block[{s = Prime@ Range@ 200, q, r}, q = Select[Partition[s, 2, 1], Differences@ # == {2} &]; r = Complement[s, Union@ Flatten@ q]; q = Mean /@ q; TakeWhile[#, IntegerQ] &@ Table[SelectFirst[q, # > p &] - p, {p, r}]] (* Michael De Vlieger, Feb 16 2018 *)
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PROG
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(PARI) {
p=2; t1=2;
forprime(t=3, 1000,
if(t-p==2,
t2=p+1;
forprime(i=t1, t2-2,
print1(t2-i, ", ")
);
t1=t2+2
);
p=t
)
}
(PARI) lista(nn) = {forprime(p=2, nn, if(!isprime(p-2)&&!isprime(p+2), forprime(q = p+1, , if (isprime(q+2), print1(q+1-p, ", "); break); ); ); ); } \\ Michel Marcus, Mar 01 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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