OFFSET
1,1
COMMENTS
Start examining the natural numbers from 2 on and call an "atom" the first integer which cannot be divided by another "atom"; this sieve produces the prime numbers. Here we call "atom" the second integer which cannot be divided by another "atom" - thus the sequence starts with 3 (not 2) and continues with 5 (not 4), then 8 (not 6 or 7), then 13, etc.
Terms computed by Mensanator.
REFERENCES
J.-P. Delahaye, La suite du lézard et autres inventions, Pour la Science, No. 353, 2007.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 150 terms from a correspondent using the pseudonym "Mensanator")
Eric Angelini, Thousand Zetas
Eric Angelini, Thousand Zetas [Cached copy, with permission]
FORMULA
Conjecture : a(n) is asymptotic to c*n*log(n) with c about 1.5. - Benoit Cloitre, Feb 11 2007
PROG
(PARI) A123929(n, mode=0/*+1=print, +2=return list*/, N=2, P=List(N+1))={ while(n--, my(k=P[#P]); for(i=1, N, while(k++, for(j=1, #P, k%P[j]||next(2)); break)); bittest(mode, 0)&&print1(k", "); listput(P, k)); if(bittest(mode, 1), Vec(P), P[#P])} \\ M. F. Hasler, Dec 24 2013
(PARI) v=vectorsmall(10^3); u=List(); v[n=1]=1; while(n<#v*99/100, while(v[n++], ); while(v[n++], ); listput(u, n); forstep(k=2*n, #v, n, v[k]=1)); Vec(u) \\ Charles R Greathouse IV, Jan 02 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Eric Angelini and Hugo van der Sanden, Nov 22 2006
STATUS
approved