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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A331467 A337289 A097431 * A036715 A337503 A310035
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified May 29 10:46 EDT 2024. Contains 372938 sequences. (Running on oeis4.)