

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
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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 nary Sieve, Smarandache Notions Journal, Vol. 10, No. 123, 1999, 146147.
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


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 !! (n1)
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

Cf. A007950, A007951, A007952.
Cf. A064801.
Sequence in context: A285160 A287321 A030366 * A026311 A063291 A088225
Adjacent sequences: A048856 A048857 A048858 * A048860 A048861 A048862


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



