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A007950 Binary sieve: delete every 2nd number, then every 4th, 8th, etc. 5
1, 3, 5, 9, 11, 13, 17, 21, 25, 27, 29, 33, 35, 37, 43, 49, 51, 53, 57, 59, 65, 67, 69, 73, 75, 77, 81, 85, 89, 91, 97, 101, 107, 109, 113, 115, 117, 121, 123, 129, 131, 133, 137, 139, 145, 149, 153, 155, 157, 161, 163, 165, 171, 173, 177, 179, 181, 185, 187, 195, 197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Comments from C. Le (charlestle(AT)yahoo.com), Mar 22 2004: "A007950 and A007951 are particular cases of the Smarandache n-ary sequence sieve (for n=2 and respectively n=3).

"Definition of Smarandache n-ary sieve (n >= 2): Starting to count on the natural numbers set at any step from 1: - delete every n-th numbers; - delete, from the remaining numbers, every (n^2)-th numbers; ... and so on: delete, from the remaining ones, every (n^k)-th numbers, k = 1, 2, 3, ... .)

"Conjectures: there are infinitely many primes that belong to this sequence; also infinitely many composite numbers.

"Smarandache general-sequence sieve: Let u_i > 1, for i = 1, 2, 3, ..., be a strictly increasing positive integer sequence. Then from the natural numbers: - keep one number among 1, 2, 3, ..., u_1 - 1 and delete every u_1 -th numbers; - keep one number among the next u_2 - 1 remaining numbers and delete every u_2 -th numbers; ... and so on, for step k (k >= 1): - keep one number among the next u_k - 1 remaining numbers and delete every u_k -th numbers; ... "

Certainly this sequence contains infinitely many composite numbers, as it has finite density A048651, while the primes have zero density.

REFERENCES

F. Smarandache, Properties of Numbers, 1972.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I.

F. Smarandache, Only Problems, Not Solutions!

Index entries for sequences generated by sieves

MATHEMATICA

t = Range@200; f[n_] := Block[{k = 2^n}, t = Delete[t, Table[{k}, {k, k, Length@t, k}]]]; Do[ f@n, {n, 6}]; t (* Robert G. Wilson v, Sep 14 2006 *)

CROSSREFS

Cf. A007951, A000959, A048651.

Sequence in context: A047623 A190523 A161781 * A034936 A204657 A167791

Adjacent sequences:  A007947 A007948 A007949 * A007951 A007952 A007953

KEYWORD

nonn

AUTHOR

R. Muller

EXTENSIONS

More terms from Robert G. Wilson v, Sep 14 2006

STATUS

approved

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Last modified February 18 00:19 EST 2019. Contains 320237 sequences. (Running on oeis4.)