A005209 Multilevel sieve: at k-th step, accept k numbers, reject k, accept k, ... (Formerly M2792)

1, 3, 9, 25, 57, 145, 337, 793, 1921, 3849, 8835, 18889, 41473, 92305, 203211, 432699, 944313, 2027529, 4077769, 8745153, 18133305, 37898113, 80713737, 169730259, 358760457, 750591867, 1575313473, 3255787851, 6751959507, 14108682265, 29364255033, 61173205587

Offset

1,2

Comments

Start with the natural numbers. For k=1,2,3,... successively do the following: accept k numbers, reject k numbers, accept k numbers, repeat indefinitely.

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..1000 [Computed using Tom Duff's bc program]

Popular Computing (Calabasas, CA), Contest 7 Results (based on solution from Tom Duff and Hugh Redelmeier), Vol. 4 (No. 43, Oct 1976), pp. 14-16. [Annotated scanned copy]

Jeffrey Shallit, Letter to N. J. A. Sloane Mar 14, 1979, concerning A001787, A005209, A005210, A005211

Index entries for sequences generated by sieves

Prog

(bc)
for(k=1; k<=100; k++){
n=k;
for(i=k-1; i>=1; --i) n=2*n-((n-1)%i)-1;
print k, " ", n, "\n"
} /* Tom Duff, Apr 24 2015 */
(Python)
from itertools import count, islice
def agen(): # generator of terms
    for k in count(1):
        n = k
        for i in range(k-1, 0, -1): n = 2*n-((n-1)%i)-1
        yield n
print(list(islice(agen(), 32))) # Michael S. Branicky, Aug 06 2022 after Tom Duff

Crossrefs

Sequence in context: A204448 A032681 A293852 * A112522 A005262 A101357

Adjacent sequences: A005206 A005207 A005208 * A005210 A005211 A005212

Keyword

nonn

Author

N. J. A. Sloane

Status

approved