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Search: id:A003312
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| A003312 |
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a(1) = 3; for n>0, a(n+1) = a(n) + [ (a(n)-1)/2 ].
(Formerly M2308)
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+0
8
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| 3, 4, 5, 7, 10, 14, 20, 29, 43, 64, 95, 142, 212, 317, 475, 712, 1067, 1600, 2399, 3598, 5396, 8093, 12139, 18208, 27311, 40966, 61448, 92171, 138256, 207383, 311074, 466610, 699914, 1049870, 1574804, 2362205, 3543307, 5314960, 7972439, 11958658, 17937986, 26906978
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence originally defined in the 1974 reference by a sieve, as follows. Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off every third term. Repeat, always crossing off every third term of those that remain. The numbers that are left form the sequence. The recurrence was found by C. L. Mallows.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
"Sieves", Popular Computing (Calabasas, CA), Vol. 2 (No. 13, Apr 1974), pp. 6-7; sieve #5.
Solution to Problem 170, Popular Computing (Calabasas, CA), Vol. 5 (No. 51, Jun 1977), pp. 17.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..500
Index entries for sequences generated by sieves
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EXAMPLE
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The first few sieving stages are as follows:
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
3 4 5 X 7 8 X 10 11 XX 13 14 XX 16 17 XX 19 20 ...
3 4 5 X 7 X X 10 11 XX XX 14 XX 16 XX XX 19 20 ...
3 4 5 X 7 X X 10 XX XX XX 14 XX 16 XX XX XX 20 ...
3 4 5 X 7 X X 10 XX XX XX 14 XX XX XX XX XX 20 ...
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MAPLE
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f:=proc(n) option remember; if n=1 then RETURN(3) fi; f(n-1)+floor( (f(n-1)-1)/2 ); end;
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CROSSREFS
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Cf. A003309, A003310, A100464, A100562, A006999, A061418, A070885, A003311.
Sequence in context: A030502 A073957 A162311 this_sequence A022440 A088130 A046840
Adjacent sequences: A003309 A003310 A003311 this_sequence A003313 A003314 A003315
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Entry revised Dec 01 2004
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