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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 l├ęzard et autres inventions, Pour la Science, No. 353, 2007.

LINKS

Mensanator and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 150 terms from 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

Cf. A126618-A126624.

Sequence in context: A331467 A337289 A097431 * A036715 A337503 A310035

Adjacent sequences:  A123926 A123927 A123928 * A123930 A123931 A123932

KEYWORD

easy,nonn

AUTHOR

Eric Angelini and Hugo van der Sanden, Nov 22 2006

STATUS

approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)