A118501 A variation on Flavius's sieves (A099204, A099243): Start with the Chen numbers; at the k-th sieving step, remove every p-th term of the sequence remaining after the (k-1)-st sieving step, where p is the k-th prime; iterate.
2, 5, 17, 23, 53, 83, 127, 167, 181, 211, 281, 347, 449, 467, 499, 509, 641, 677, 821, 887, 941, 953, 1097, 1193, 1283, 1327, 1399, 1471, 1583, 1721, 1949, 2029, 2111, 2213, 2351, 2381, 2447, 2549, 2609, 2777, 3061, 3137, 3257, 3307, 3511, 3539, 3797
Offset: 1
Keywords
Examples
Start with 2 3 5 7 11 13 17 19 23 29 31 37 41 47 53 59 67 71 83 89 101 107 109 113 127 131 ... and delete every second term, giving 2 5 11 17 23 31 41 53 67 83 101 109 127 ... and delete every 3rd term, giving 2 5 17 23 41 53 83 101 127 ... and delete every 5th term, giving 2 5 17 23 53 83 101 127 .... Continue forever and what's left is the sequence.
Programs
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Maple
ts_chen:= proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if ( isprime(i) = 'true') then if ( isprime(i+2) = 'true' or numtheory[bigomega](i+2) = 2) then ans:=[ op(ans), i ] fi fi od: return ans end: S[1]:=convert(ts_chen(25000), set): for n from 2 to 390 do S[n]:=S[n-1] minus {seq(S[n-1][ithprime(n-1)*i], i=1..nops(S[n-1])/ithprime(n-1))} od: convert(S[390],list); -
Mathematica
cp=SequencePosition[PrimeOmega[Range[3800]], {1, , 1|2}][[All, 1]] ;s={}; ps=Prime[Range[100]]; l=Range[400]; Do[l=Drop[l, {First[ps], -1, First[ps]}]; ps=Rest[ps], {17}]; Do[AppendTo[s,cp[[l[[n]]]]] ,{n,47}];s (* _James C. McMahon, Sep 19 2024 *)