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%I #4 Mar 30 2012 18:36:51
%S 1,6,31,96,241,546,1171,1776,2761,5046,7591,11856,19021,20706,31711,
%T 44016,60481,71946,92191,120216,138601,181986,226831,302496,379381,
%U 400686,487831,574656,704461,831606,1029631,1092936,1333321,1462146
%N Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 4 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
%C Formula: a(n) = 1 + [..[[[[n*2/1]3/2]4/3]5/4]...(k+1)/k]...] where denominators k of the fractions used in the product vary over all natural numbers not congruent to 0 (mod 5); thus the product will eventually reach a maximum value of a(n).
%F a(n) = 1 + 5*A073362(n).
%e Sieve starts with the natural numbers:
%e 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,...
%e Step 1: keep 1 term, remove the next 4, repeat; giving
%e 1,6,11,16,21,26,31,36,41,46,51,56,61,66,...
%e Step 2: keep 2 terms, remove the next 4, repeat; giving
%e 1,6,31,36,61,66,91,96,121,126,151,156,...
%e Step 3: keep 3 terms, remove the next 4, repeat; giving
%e 1,6,31,96,121,126,211,216,241,306,331,...
%e Continuing in this way, we obtain this sequence.
%e Using the floor function product formula:
%e a(2) = 1 + [..[(2)*2/1]*3/2]*4/3]*6/5]*7/6]*8/7]*10/9]*
%e 11/10]*12/11]*14/13]*15/14]*16/15]*18/17]*19/18]*20/19] = 21.
%o (PARI) {a(n)=local(A=n,B=0,k=0); until(A==B,k=k+1;if(k%5==0,k=k+1);B=A;A=floor(A*(k+1)/k));1+A}
%Y Cf. A073362, A112560, A112561, A112563, A112564, A112565, A112566, A112567, A112568, A112569.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 14 2005
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