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A097977
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Smallest prime p such that p+n is the product of exactly n distinct primes.
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3
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2, 13, 67, 1151, 9277, 1616609, 1874723, 111546427, 2751478721, 862410107549, 747543645019, 3080843115635273, 1006366256282297, 2679162624135569701, 166366498382137547479, 993969333554296364249, 8302567374394710807373
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OFFSET
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1,1
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COMMENTS
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The sequence goes on with a(18, 19, 20, ...) = 112733682549950000276752997, 32674073817649531442865671, 376147205196163170923414109829, ... - M. F. Hasler, Jan 14 2012
The terms are of the form a(n)=A002110(n+k)/Q - n, where Q is the product of k among the first n+k-1 primes, and these k primes include all prime factors of n, cf. examples. - M. F. Hasler, Jan 14 2012
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LINKS
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EXAMPLE
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a(4)=1151, for example, is the first of a sequence of primes that continues with 1361, 2141, 2411, 2801, 3251, 3881, 3923, ...with the property 1151+4=3*5*7*11, 1361+4=3*5*7*13, 2141+5=3*5*11*13, 2801+4=3*5*11*17, 3251+4=3*5*7*31, 3881+4=3*5*7*37, 3923+4=3*7*11*17, ...
The terms can be written a(n)=A002110(n+k)/Q-n (cf. comment) as follows:
etc.
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MATHEMATICA
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Table[k := 1; While[Not[Length[FactorInteger[Prime[k] + n]] == n], k++ ]; Prime[k], {n, 1, 7}] (* Stefan Steinerberger, Apr 03 2006 *)
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PROG
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(PARI) A097977(n, show=0, LIM=9)={ my(P=A002110(n), M); for(i=0, LIM, i && P*=prime(n+i); forvec(v=vector(i, j, [1, n+i-1]), t=P/prod(j=1, #v, prime(n+i-v[j]))-n; M && t>=M && (v[#v]+=n+i) && next; isprime(t) || next; M=t; show && print([t, i, v]), 2)); M} \\ M. F. Hasler, Jan 14 2012
(Haskell)
a097977 n = head [p | p <- dropWhile (<= n) a000040_list,
a001221 (p + n) == n]
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CROSSREFS
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KEYWORD
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hard,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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