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A350828
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Number of prime octuplets with initial member (A065706) between 10^(n-1) and 10^n.
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3
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0, 2, 0, 1, 1, 3, 3, 9, 28, 136, 541, 2936
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OFFSET
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1,2
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COMMENTS
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"Between 10^(n-1) and 10^n" is equivalent to saying "with n (decimal) digits".
A prime octuplet is a sequence of 8 consecutive primes (p1, ..., p8) of minimal diameter p8 - p1 = 26.
Terms a(1)-a(12) computed from b-file a(1..18123) for A065706. Using Luhn's database, cf. LINKS, one can get 3 more terms.
So far, the last term of all the octuplets has the same number of digits as the initial term.
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LINKS
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EXAMPLE
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a(1) = a(3) = 0 because there is no single-digit nor a 3-digit prime initial member of a prime octuplet.
a(2) = 2 because 11 and 17 are the only 2-digit members of A065706, i.e., primes to start a prime octuplet.
a(4) = a(5) = 1 because 1277 (resp. 88793) is the only prime with 4 (resp. 5) digits to start a prime octuplet.
Then there are a(6) = 3 six-digit primes, 113147, 284723 and 855713, which start a prime octuplet.
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PROG
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(PARI) (D(v)=v[^1]-v[^-1])( [setsearch(A065706, 10^n, 1) | n<-[0..12]] ) \\ where A065706 is a vector of at least 3660 terms of that sequence.
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CROSSREFS
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Cf. A065706 (initial members p of prime octuplets (p, ..., p+26)), A022011, A022012, A022013 (idem, specifically for each of the three possible patterns).
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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STATUS
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approved
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