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Iterated golden sieve: Iterate indefinitively the procedure giving A099267 (S2) from the natural numbers (S1) with the single difference that the rank of the deleted terms is f(n) + (p-2) to get Sp from Sp-1.
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%I #9 Jul 19 2021 01:20:16

%S 2,3,6,11,18,27,39,53,69,81,87,113,141,171,204,241,277,304,336,372,

%T 410,432,442,476,512,543,592,622,657,700,739,775,808,855,897,934,984,

%U 1021,1069,1106,1155,1199,1247,1297,1341,1388,1440,1490,1538,1592,1640,1686

%N Iterated golden sieve: Iterate indefinitively the procedure giving A099267 (S2) from the natural numbers (S1) with the single difference that the rank of the deleted terms is f(n) + (p-2) to get Sp from Sp-1.

%e S1 = 1,2,3,4,5,6,7,_,9,10,11,12,13,

%e S2 = A099267 = 2,3,5,6,8,10,11,13,14,16,18

%e S3: in S2 (3-2)+f(1)=3, then 5 is deleted, remaining 2,3,6,8,10,11,13,14,16,18

%e in this remaining sequence (3-2)+f(2)=4, then 8 is deleted, leaving 2,3,6,10,11,13,14,16,18

%e ....

%e The first two terms of S2 are definitively safe. It's the same for the first three of S3, and so on;

%e Iterating indefinitely the procedure produces the sequence: 2,3,6,11,18,27,39,53,69,81,87,113 where the first p terms are already the first p terms of Sp and all following sequences.

%Y Cf. A099267.

%K easy,nonn

%O 1,1

%A Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Aug 14 2007