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A039672 Fibonacci-lucky numbers: generated by a sieve process with Fibonacci rule.

%I A039672 #16 Jul 13 2013 12:02:03
%S A039672 1,2,4,5,7,10,11,13,16,19,20,23,25,28,29,32,37,38,40,41,49,50,52,56,
%T A039672 58,59,61,65,68,74,76,77,82,83,86,88,91,97,101,103,104,106,115,118,
%U A039672 121,122,124,130,131,133,136,137,149,151,154,155,158,163,164,166,173,175
%N A039672 Fibonacci-lucky numbers: generated by a sieve process with Fibonacci rule.
%C A039672 Start with 1 2 3 4 5 6 7 8 9 10 11 12 13...; sum of first and 2nd terms = 3; strike out every 3rd term: 1 2 4 5 7 8 10 11 13...; sum of 2nd and 3rd terms = 6; strike out every 6th term: 1 2 4 5 7 10 11 13...; sum of 3rd and 4th terms = 9; strike out every 9th number; etc.
%H A039672 Reinhard Zumkeller, <a href="/A039672/b039672.txt">Table of n, a(n) for n = 1..400</a>
%H A039672 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%t A039672 Fold[ Delete[ #1, Thread[ List[ Rest[ Range[ 0, Length[ #1 ], #1[ [ #2 ] ]+#1[ [ #2+1 ] ] ] ] ] ] ]&, Range[ 200 ], Range[ 20 ] ]
%o A039672 (Haskell)
%o A039672 a039672 n = a039672_list !! (n-1)
%o A039672 a039672_list = sieve 1 [1..] where
%o A039672    sieve k xs = z : sieve (k + 1) (fLucky xs) where
%o A039672       z = xs !! (k - 1 )
%o A039672       fLucky ws = us ++ fLucky vs where
%o A039672              (us, _:vs) = splitAt (z + xs !! k - 1) ws
%o A039672 -- _Reinhard Zumkeller_, Dec 05 2011
%Y A039672 Cf. A000959, A039681.
%K A039672 nice,nonn
%O A039672 1,2
%A A039672 _Felice Russo_
%E A039672 Corrected by Larry Reeves (larryr(AT)acm.org), Feb 21 2001