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

42, 52, 76, 92, 116, 117, 125, 174, 182, 186, 212, 230, 266, 275, 282, 285, 316, 318, 325, 385, 406, 410, 423, 428, 436, 455, 470, 474, 507, 508, 534, 575, 604, 605, 618, 627, 654, 657, 670, 678, 682, 705, 710, 730, 754, 762, 772, 788, 834, 861, 903, 931

Offset: 1

Author

Jonathan Vos Post, Apr 30 2005

Keywords

• easy
• nonn

Comments

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.

Examples

			a(1) = 3-almost-prime(3-almost-prime(1)) = 3-almost-prime(8) = 42.
a(2) = 3-almost-prime(3-almost-prime(2)) = 3-almost-prime(12) = 52.
a(3) = 3-almost-prime(3-almost-prime(3)) = 3-almost-prime(18) = 76.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Almost Prime.

Crossrefs

Cf. A014612, A000040, A001358, A007097, A091022, A105997, A105998, A101349, A106350.

Programs

Maple

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

Mathematica

With[{tap=Select[Range[2000],PrimeOmega[#]==3&]},Table[tap[[tap[[n]]]],{n,100}]] (* Harvey P. Dale, May 20 2019 *)

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

Formula

a(n) = A014612(A014612(n)).

Extensions

Extended by R. J. Mathar, Jan 27 2009