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

1, 2, 4, 5, 7, 10, 11, 13, 16, 19, 20, 23, 25, 28, 29, 32, 37, 38, 40, 41, 49, 50, 52, 56, 58, 59, 61, 65, 68, 74, 76, 77, 82, 83, 86, 88, 91, 97, 101, 103, 104, 106, 115, 118, 121, 122, 124, 130, 131, 133, 136, 137, 149, 151, 154, 155, 158, 163, 164, 166, 173, 175

Offset: 1

Author

Felice Russo

Keywords

• nice
• nonn

Comments

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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..400
• Index entries for sequences generated by sieves

Crossrefs

Cf. A000959, A039681.

Programs

Haskell

a039672 n = a039672_list !! (n-1)
a039672_list = sieve 1 [1..] where
   sieve k xs = z : sieve (k + 1) (fLucky xs) where
      z = xs !! (k - 1 )
      fLucky ws = us ++ fLucky vs where
             (us, _:vs) = splitAt (z + xs !! k - 1) ws
-- Reinhard Zumkeller, Dec 05 2011

Mathematica

Fold[ Delete[ #1, Thread[ List[ Rest[ Range[ 0, Length[ #1 ], #1[ [ #2 ] ]+#1[ [ #2+1 ] ] ] ] ] ] ]&, Range[ 200 ], Range[ 20 ] ]

Extensions

Corrected by Larry Reeves (larryr(AT)acm.org), Feb 21 2001