

A007950


Binary sieve: delete every 2nd number, then every 4th, 8th, etc.


6



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
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OFFSET

1,2


COMMENTS

Comments from C. Le (charlestle(AT)yahoo.com), Mar 22 2004: "A007950 and A007951 are particular cases of the Smarandache nary sequence sieve (for n=2 and respectively n=3).
"Definition of Smarandache nary sieve (n >= 2): Starting to count on the natural numbers set at any step from 1:  delete every nth 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 generalsequence 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!, 4th ed., 1993, Problem 95.
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



