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, ...

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

Author

Charles T. Le (charlestle(AT)yahoo.com)

Keywords

• nonn

Examples

			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.
		

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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I.
• Index entries for sequences generated by sieves

Crossrefs

Cf. A007950, A007951, A007952.

Cf. A064801.

Programs

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

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 *)

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