1,2

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; ... "

F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993

C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I, Erhus Publ., Glendale, 1994.

F. Smarandache, Properties of Numbers, 1972.

M. L. Perez et al., eds., Smarandache Notions Journal

F. Smarandache, Only Problems, Not Solutions!

Index entries for sequences generated by sieves

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

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

Cf. A007951, A000959.

Adjacent sequences: A007947 A007948 A007949 this_sequence A007951 A007952 A007953

Sequence in context: A066769 A088607 A047623 this_sequence A034936 A003071 A109324

nonn

R. Muller

More terms from Robert G. Wilson v Sep 14 2006