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A123929
Simili-primes of order 2.
10
3, 5, 8, 13, 17, 22, 28, 31, 38, 43, 47, 53, 59, 67, 73, 77, 82, 89, 97, 101, 107, 113, 121, 127, 133, 139, 148, 151, 158, 163, 167, 179, 191, 197, 203, 209, 218, 227, 233, 241, 251, 257, 262, 269, 274, 281, 284, 293, 307, 313, 317, 322, 332, 343, 347, 353, 361
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
STATUS
approved