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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
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
MATHEMATICA
With[{tap=Select[Range[2000], PrimeOmega[#]==3&]}, Table[tap[[tap[[n]]]], {n, 100}]] (* Harvey P. Dale, May 20 2019 *)
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Apr 30 2005
EXTENSIONS
Extended by R. J. Mathar, Jan 27 2009
STATUS
approved