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A006094
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Products of 2 successive primes.
(Formerly M4110)
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63
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6, 15, 35, 77, 143, 221, 323, 437, 667, 899, 1147, 1517, 1763, 2021, 2491, 3127, 3599, 4087, 4757, 5183, 5767, 6557, 7387, 8633, 9797, 10403, 11021, 11663, 12317, 14351, 16637, 17947, 19043, 20711, 22499, 23707, 25591, 27221, 28891, 30967, 32399
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The Huntley reference would suggest prefixing the sequence with an initial 4 - Enoch Haga (Enokh(AT)comcast.net). [But that would conflict with the definition! - N. J. A. Sloane, Oct 13 2009]
Sequence appears to coincide with the sequence of numbers n such that the largest prime < sqrt(n) and the smallest prime > sqrt(n) divide n. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 04 2002
a(n+1) = smallest number such that GCD ( a(n), a(n+1) ) = prime(n+1). - Alexandre Wajnberg and Ray Chandler (alexandre.wajnberg(AT)skynet.be), Oct 14 2005
Also the area of rectangles whose side lengths are consecutive primes. E.g. The consecutive primes 7,11 produce a 7x11 unit rectangle which has area 77 square units. - Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
a(n)=a001358(A172348(n)); A046301(n)=LCM(a(n),a(n+1)); A065091(n)=GCD(a(n),a(n+1)); A066116(n+2)=a(n+1)*a(n); A109805(n)=a(n+1)-a(n). [Reinhard Zumkeller, Mar 13 2011]
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REFERENCES
| H. E. Huntley, The Divine Proportion, A Study in Mathematical Beauty. New York: Dover, 1970. See Chapter 13, Spira Mirabilis, especially Fig. 13-5, page 173.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
| Table[ Prime[n] Prime[n + 1], {n, 1, 40}] (from Robert G. Wilson v Jan 22 2004)
Times@@@Partition[Prime[Range[60]], 2, 1] (* From Harvey P. Dale, Oct 15 2011 *)
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PROG
| (PARI) g(n) = for(x=1, n, print1(prime(x)*prime(x+1)", ")) - Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
(Mupad) ithprime(i)*ithprime(i+1) $ i = 1..41 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 26 2007
(SAGE) BB = primes_first_n(56) list = [] for i in range(55): list.append(BB[1+i]*BB[i]) list - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2007
(MAGMA) [NthPrime(n)*NthPrime(n+1): n in [1..41]]; // Bruno Berselli, Feb 24 2011
(Haskell)
a006094 n = a006094_list !! (n-1)
a006094_list = zipWith (*) a000040_list a065091_list
-- Reinhard Zumkeller, Mar 13 2011
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CROSSREFS
| Subset of the squarefree semiprimes, A006881. Cf. A090076, A090090.
Cf. A166329, A152241, A030664.
Cf. A046301, A046302, A046303, A046324, A046325, A046326, A046327.
Sequence in context: A049728 A038666 A075625 * A099620 A045969 A100513
Adjacent sequences: A006091 A006092 A006093 * A006095 A006096 A006097
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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