1,1

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 consecutive prime rectangles. A consecutive prime rectangle is a rectangle whose sides are components of 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

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).

T. D. Noe, Table of n, a(n) for n=1..1000

Table[ Prime[n] Prime[n + 1], {n, 1, 40}] (from Robert G. Wilson v Jan 22 2004)

(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

Subset of the square-free semiprimes, A006881. Cf. A090076, A090090.

Cf. A166329, A152241.

Sequence in context: A049728 A038666 A075625 this_sequence A099620 A045969 A100513

Adjacent sequences: A006091 A006092 A006093 this_sequence A006095 A006096 A006097

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).