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A105346 3-almost primes whose indices are 3-almost primes.

%I A105346 #14 Feb 16 2025 08:32:57
%S A105346 42,52,76,92,116,117,125,174,182,186,212,230,266,275,282,285,316,318,
%T A105346 325,385,406,410,423,428,436,455,470,474,507,508,534,575,604,605,618,
%U A105346 627,654,657,670,678,682,705,710,730,754,762,772,788,834,861,903,931
%N A105346 3-almost primes whose indices are 3-almost primes.
%C A105346 The n-th 3-almost prime function applied to itself. This is the 3-almost prime equivalent of A091022, the latter being the n-th 2-almost prime function applied to itself. Note that this new iterated 3-almost prime sequence begins with the meaning of "Life, the Universe and Everything" and then generalizes to include the number of playing cards in a deck and the boiling point of water on the Fahrenheit scale.
%H A105346 Charles R Greathouse IV, <a href="/A105346/b105346.txt">Table of n, a(n) for n = 1..10000</a>
%H A105346 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%F A105346 a(n) = A014612(A014612(n)).
%e A105346 a(1) = 3-almost-prime(3-almost-prime(1)) = 3-almost-prime(8) = 42.
%e A105346 a(2) = 3-almost-prime(3-almost-prime(2)) = 3-almost-prime(12) = 52.
%e A105346 a(3) = 3-almost-prime(3-almost-prime(3)) = 3-almost-prime(18) = 76.
%p A105346 isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: A014612 := proc(n) option remember ; if n =1 then 8; else for a from procname(n-1)+1 do if isA014612(a) then RETURN(a) ; fi; od; fi; end: for n from 1 to 100 do q := A014612(A014612(n)) ; printf("%d,",q) ; od: # _R. J. Mathar_, Jan 27 2009
%t A105346 With[{tap=Select[Range[2000],PrimeOmega[#]==3&]},Table[tap[[tap[[n]]]],{n,100}]] (* _Harvey P. Dale_, May 20 2019 *)
%o A105346 (PARI) do(lim)=my(v=List(), t); forprime(p=2, lim\4, forprime(q=2, min(lim\(2*p), p), t=p*q; forprime(r=2, min(lim\t, q), listput(v, t*r)))); v=Set(v); t=setsearch(v,#v); if(!t, t=setsearch(v,#v,1)-1); vector(t,i,v[v[i]]) \\ _Charles R Greathouse IV_, Feb 05 2017
%Y A105346 Cf. A014612, A000040, A001358, A007097, A091022, A105997, A105998, A101349, A106350.
%K A105346 easy,nonn
%O A105346 1,1
%A A105346 _Jonathan Vos Post_, Apr 30 2005
%E A105346 Extended by _R. J. Mathar_, Jan 27 2009