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

1,1

Comments

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

Links

Table of n, a(n) for n=1..46.

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 *)

Crossrefs

Cf. A000695.

Sequence in context: A344061 A045680 A174352 * A026678 A026869 A350662

Adjacent sequences: A152018 A152019 A152020 * A152022 A152023 A152024

Keyword

nonn

Author

Vladimir Shevelev, Nov 20 2008

Extensions

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

More terms from Amiram Eldar, Aug 31 2019

Status

approved