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A152021 Numbers a(n) are obtained by the direct application of sieve of Eratosthenes for A000695: retaining A000695(2)=4, we delete all multiples of 4, which are more than 4; retaining A000695(3)=5, we delete all multiples of 5, which are more than 5, etc.

%I A152021 #8 Sep 01 2019 02:36:01
%S A152021 4,5,17,21,69,81,257,261,277,321,337,341,1041,1089,1093,1109,1297,
%T A152021 1301,1349,1361,4101,4113,4117,4161,4177,4181,4353,4357,4373,4417,
%U A152021 4421,5121,5137,5141,5189,5201,5377,5381,5393,5441,5461,16389,16449,16453,16469,16641
%N A152021 Numbers a(n) are obtained by the direct application of sieve of Eratosthenes for A000695: retaining A000695(2)=4, we delete all multiples of 4, which are more than 4; retaining A000695(3)=5, we delete all multiples of 5, which are more than 5, etc.
%C A152021 If p is prime, then A000695(p) is in the sequence; but, e. g., A000695(25), A000695(55) are also in the sequence.
%p A152021 Contribution from _R. J. Mathar_, Oct 29 2010: (Start)
%p A152021 A000695 := proc(n) local dgsa ; if n= 0 then 0; else for a from procname(n-1)+1 do dgsa := convert(convert(a,base,4),set) ; if dgsa minus {0,1} = {} then return a; end if; end do: end if; end proc:
%p A152021 A152021 := proc(nmax) a := [seq(A000695(i),i=2..nmax)] ; ptr := 1; while ptr < nops(a) do for j from nops(a) to ptr+1 by -1 do if op(j,a) mod op(ptr,a) = 0 then a := subsop(j=NULL,a) ; end if; end do: ptr := ptr+1 ; end do: a ; end proc: A152021(120) ; (End)
%t A152021 f[n_] := FromDigits[IntegerDigits[n, 2], 4]; s = Array[f, 150, 2]; div[a_, b_] := Divisible[a, b] && a > b; n = 1; While[Length[s] > n, s = Select[s, !div[#, s[[n]]] &]; n++]; s (* _Amiram Eldar_, Aug 31 2019 *)
%Y A152021 Cf. A000695.
%K A152021 nonn
%O A152021 1,1
%A A152021 _Vladimir Shevelev_, Nov 20 2008
%E A152021 More terms from _R. J. Mathar_, Oct 29 2010
%E A152021 More terms from _Amiram Eldar_, Aug 31 2019