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A048859
A sieve: keep the first 2 numbers, delete the next 3 numbers; keep the next 3 numbers, delete the next 4 numbers; keep the next 4 numbers, delete the next 5 numbers; and so on. In other words, keep the next k numbers and delete the next k+1 numbers, for k = 2, 3, ...
5
1, 2, 6, 7, 8, 13, 14, 15, 16, 22, 23, 24, 25, 26, 33, 34, 35, 36, 37, 38, 46, 47, 48, 49, 50, 51, 52, 61, 62, 63, 64, 65, 66, 67, 68, 78, 79, 80, 81, 82, 83, 84, 85, 86, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128
OFFSET
1,2
REFERENCES
C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I, Erhus Publ., Glendale, 1994.
M. Le, On the Smarandache n-ary Sieve, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 146-147.
F. Smarandache, Properties of Numbers, 1972.
EXAMPLE
List the natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...
Keep the first two numbers 1, 2 and delete the next three numbers 3, 4, 5.
Keep the next three numbers 6, 7, 8 and delete the next four numbers 9, 10, 11, 12. And so on.
MATHEMATICA
ss[n_]:=Module[{c=n^2+4n+1}, Range[c, c+n+1]]; Flatten[Array[ss, 10, 0]] (* Harvey P. Dale, Sep 10 2014 *)
PROG
(Haskell)
a048859 n = a048859_list !! (n-1)
a048859_list = f 2 [1..] where
f k xs = us ++ f (k + 1) (drop (k + 1) vs)
where (us, vs) = splitAt k xs
-- Reinhard Zumkeller, May 16 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles T. Le (charlestle(AT)yahoo.com)
EXTENSIONS
Corrected and revised by the author, Mar 24 2004
More terms from Bernardo Boncompagni Jul 27 2004
Offset changed by Reinhard Zumkeller, May 16 2014
STATUS
approved