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.

4, 5, 17, 21, 69, 81, 257, 261, 277, 321, 337, 341, 1041, 1089, 1093, 1109, 1297, 1301, 1349, 1361, 4101, 4113, 4117, 4161, 4177, 4181, 4353, 4357, 4373, 4417, 4421, 5121, 5137, 5141, 5189, 5201, 5377, 5381, 5393, 5441, 5461, 16389, 16449, 16453, 16469, 16641

Offset: 1

Author

Vladimir Shevelev, Nov 20 2008

Keywords

• nonn

Comments

If p is prime, then A000695(p) is in the sequence; but, e. g., A000695(25), A000695(55) are also in the sequence.

Crossrefs

Cf. A000695.

Programs

Maple

Contribution from R. J. Mathar, Oct 29 2010: (Start)
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:
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)

Mathematica

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 *)

Extensions

More terms from R. J. Mathar, Oct 29 2010

More terms from Amiram Eldar, Aug 31 2019