A123929 - OEIS

%I #27 Apr 09 2023 02:15:46

%S 3,5,8,13,17,22,28,31,38,43,47,53,59,67,73,77,82,89,97,101,107,113,

%T 121,127,133,139,148,151,158,163,167,179,191,197,203,209,218,227,233,

%U 241,251,257,262,269,274,281,284,293,307,313,317,322,332,343,347,353,361

%N Simili-primes of order 2.

%C 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.

%C Terms computed by Mensanator.

%D J.-P. Delahaye, La suite du lézard et autres inventions, Pour la Science, No. 353, 2007.

%H Charles R Greathouse IV, <a href="/A123929/b123929.txt">Table of n, a(n) for n = 1..10000</a> (first 150 terms from a correspondent using the pseudonym "Mensanator")

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/ThousandZetas.htm">Thousand Zetas</a>

%H Eric Angelini, <a href="/A123929/a123929.html">Thousand Zetas</a> [Cached copy, with permission]

%F Conjecture : a(n) is asymptotic to c*n*log(n) with c about 1.5. - _Benoit Cloitre_, Feb 11 2007

%o (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

%o (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

%Y Cf. A126618-A126624.

%K easy,nonn

%O 1,1

%A _Eric Angelini_ and _Hugo van der Sanden_, Nov 22 2006