A045954 Even-Lucky-Numbers: generated by a sieve process like that for Lucky numbers but starting with even numbers.

2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76, 84, 90, 98, 100, 102, 108, 114, 116, 118, 130, 132, 138, 140, 148, 150, 164, 170, 172, 178, 182, 186, 196, 198, 212, 214, 218, 228, 230, 234, 244, 246, 260, 262, 268, 278, 282, 290, 298, 300, 308

Offset

1,1

Comments

Write down even numbers: 2, 4, 6, 8, ...; first term > 2 is 4 so starting from 2 remove every 4th number: 2, 4, 6, 10, 12, 14, 18, ...; next number is 6 so remove every 6th term starting from 2: 2, 4, 6, 10, 12, 18, 20, 22, 26, etc.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for sequences generated by sieves

Maple

## Finds all Even Lucky Numbers up to n from the list 2..n.
## Try n=10^5 or 10^6 just for fun!
evenluckynumbers:=proc(n) local k, Lnext, Lprev; Lprev:=[$2..n]; for k from 1 do Lnext:= map(w-> Lprev[w], remove(z -> z mod Lprev[k] = 0, [$1..nops(Lprev)])); if nops(Lnext)=nops(Lprev) then return Lnext fi; Lprev:=Lnext; od; end: # Walter Kehowski, Jun 06 2008

Mathematica

lst = Range[2, 308, 2]; i = 2; While[ i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; lst (* Robert G. Wilson v, May 11 2006 *)

Prog

(Haskell)
a045954 n = a045954_list !! (n-1)
a045954_list =  2 : sieve 2 [2, 4..] where
   sieve k xs = z : sieve (k + 1) (lucky xs) where
      z = xs !! (k - 1 )
      lucky ws = us ++ lucky vs where
            (us, _:vs) = splitAt (z - 1) ws
-- Reinhard Zumkeller, Dec 05 2011

Crossrefs

Cf. A000959, A039672.

Sequence in context: A033098 A220478 A033868 * A072542 A167856 A293750

Adjacent sequences: A045951 A045952 A045953 * A045955 A045956 A045957

Keyword

nice,nonn,easy

Author

Felice Russo

Status

approved