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A105346 3-almost primes whose indices are 3-almost primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Almost Prime.

FORMULA

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

EXAMPLE

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.

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

PROG

(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

CROSSREFS

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

Sequence in context: A255513 A186456 A181647 * A108119 A175103 A116262

Adjacent sequences:  A105343 A105344 A105345 * A105347 A105348 A105349

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Apr 30 2005

EXTENSIONS

Extended by R. J. Mathar, Jan 27 2009

STATUS

approved

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Last modified February 22 19:54 EST 2019. Contains 320403 sequences. (Running on oeis4.)