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%I #12 Oct 04 2021 13:38:07
%S 1,2,3,5,7,10,14,19,26,35,47,63,85,114,153,205,274,366,489,653,871,
%T 1162,1550,2067,2757,3677,4903,6538,8718,11625,15501,20669,27559,
%U 36746,48995,65327,87103,116138,154851,206469
%N (L)-sieve transform of A004767 = {3,7,11,15,...,4n-1,...}.
%C See A152009 for the definition of the (L)-sieve transform.
%C This appears to be the same sequence that is defined in Problem 193 of Popular Computing, Number 55 (see link). - _N. J. A. Sloane_, Apr 16 2015
%H Popular Computing (Calabasas, CA), <a href="/A155167/a155167.pdf">Coding Fun: Rearranging All The Numbers</a>, Annotated and scanned copy of pages PC55-2, PC55-3, and PC55-1(cover) of Vol. 5 (No. 55, Oct 1977).
%F All listed terms satisfy the recurrence a(n)=Floor[(4*a[[n-1]]+3)/3], with a(1)=1.
%p # Maple program for Popular Computing Problem 193, which produces terms which appear to match this sequence, from _N. J. A. Sloane_, Apr 16 2015
%p with(LinearAlgebra): M:=1000; B:=300;
%p t1:=Array(1..M,0); t2:=Array(1..M,0); t3:=Array(1..M,-1);
%p for n from 1 to M do t1[n]:=n+2; od:
%p for n from 1 to B do
%p i:=t1[1];
%p if t3[i] = -1 then t3[i]:=n-1; fi;
%p for j from 1 to i do t2[j]:=t1[j+1]; od:
%p t2[i+1]:=i;
%p for p from i+2 to M-2 do t2[p]:=t1[p]; od;
%p for q from 1 to M-2 do t1[q]:=t2[q]; od:
%p od:
%p [seq(t3[n],n=3..B)];
%t NestList[Floor[(4#+3)/3]&,1,40] (* _Harvey P. Dale_, Oct 04 2021 *)
%Y Cf. A004767, A006999, A061419, A152009.
%K nonn
%O 1,2
%A _John W. Layman_, Jan 21 2009
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