Search: id:A099361
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%I A099361
%S A099361 2,3,7,13,29,37,53,79,89,107,113,139,151,173,181,223,239,251,311,317,
%T A099361 349,359,383,397,421,463,491,503,541,577,593,613,619,647,659,683,743,
%U A099361 787,821,857,863,887,911,983,997,1033,1061,1151,1163,1193,1213,1249
%N A099361 A variation on the sieve of Eratosthenes (A00040): Start with the primes; 
               the first term is 2, which is a(1) and we cross off every second 
               prime starting with 2; the next prime not crossed off is 3, which 
               is a(2) and we cross off every third prime starting with 3; the next 
               prime not crossed off is 7, which is a(3) and we cross off every 
               7-th prime starting with 7; and so on.
%C A099361 In contrast to Flavius's sieve (A000960), primes are not erased when 
               they are crossed off; that is, primes get crossed off multiple times 
               (see A099362).
%H A099361 T. D. Noe, <a href="b099361.txt">Table of n, a(n) for n=1..1000</a>
%H A099361 <a href="Sindx_Si.html#sieve">Index entries for sequences generated by 
               sieves</a>
%e A099361 The first few sieving stages are as follows (X or XX indicates a prime 
               that has been crossed off one or more times):
%e A099361 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 
               ...
%e A099361 2 3 X 7 XX 13 XX 19 XX 29 XX 37 XX 43 XX 53 XX 61 XX 71 XX 79 XX 89 XX 
               ...
%e A099361 2 3 X 7 XX 13 XX XX XX 29 XX 37 XX XX XX 53 XX 61 XX XX XX 79 XX 89 XX 
               ...
%e A099361 2 3 X 7 XX 13 XX XX XX 29 XX 37 XX XX XX 53 XX XX XX XX XX 79 XX 89 XX 
               ...
%e A099361 .... Continue for ever and the numbers not crossed off give the sequence.
%t A099361 nn=300; a=Prime[Range[nn]]; Do[p=a[[i]]; If[p>0, Do[a[[j]]=0, {j, i+p, 
               nn, p}]], {i, nn}]; Rest[Union[a]] (T. D. Noe)
%Y A099361 Cf. A000040, A000960, A099204, A099207, A099243, A099362.
%Y A099361 Cf. A100424
%Y A099361 Sequence in context: A006946 A074129 A055003 this_sequence A113823 A113843 
               A113884
%Y A099361 Adjacent sequences: A099358 A099359 A099360 this_sequence A099362 A099363 
               A099364
%K A099361 nonn,easy,nice
%O A099361 1,1
%A A099361 N. J. A. Sloane (njas(AT)research.att.com), Nov 18 2004
%E A099361 More terms from T. D. Noe (noe(AT)sspectra.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), 
               Nov 18 2004

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