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Search: id:A136106
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| A136106 |
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a(n) = smallest prime p such that in the sequence of n numbers p, p+1, p+2, ..., p+n-1, the i-th terms is the product of i distinct primes, for i = 1, ..., n. |
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1
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OFFSET
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1,1
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FORMULA
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a(n) >= A086560(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2008
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EXAMPLE
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a(4)=1867 because it begins with the prime 1867 (considered as just one divisor) followed by 1868 with two prime factors, 2 and 467; then 1869 with three prime factors, 3, 7, 89; then 1870 with four prime factors, 2, 5, 11,17.
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PROGRAM
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(PARI) /* a brute force program */ a136106(st, ed, ct)={ forprime(x=st, ed, if ((x%6)!=1, next); goodFlag = 1; c = 1; while(goodFlag, if (!(c%2) && isprime(x+c), goodFlag=0, v = factor(x+c); if (length(v[, 2]) == c+1, c+=1; if (c > ct, print("Level = ", c, " at ", x+c-1, "=", v); ct+=1), goodFlag = 0 ) ) ) ); } -Fred Schneider (frederick.william.schneider(AT)gmail.com), Dec 18 2007
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CROSSREFS
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Cf. A072875.
Sequence in context: A066618 A027720 A132482 this_sequence A122696 A023263 A070855
Adjacent sequences: A136103 A136104 A136105 this_sequence A136107 A136108 A136109
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KEYWORD
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easy,more,nonn
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AUTHOR
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Enoch Haga (Enokh(AT)comcast.net), Dec 14 2007
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 23 2007
2 more terms from Fred Schneider (frederick.william.schneider(AT)gmail.com), Dec 18 2007
a(7) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 19 2009
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