This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072583 #14 Jul 28 2025 03:10:53
%S A072583 2,4,9,10,11,12,14,15,17,18,27,29,33,35,36,38,39,40,43,46,48,51,52,53,
%T A072583 54,55,56,63,66,72,73,75,76,83,85,86,90,91,92,95,96,97,100,102,104,
%U A072583 109,111,112,113,115,117,119,120,122,123,124,126,127,129,130,131,132,133
%N A072583 Numbers k with the property that there is no match when comparing the numbers of 0's and 1's in the binary representations of k and the k-th prime.
%C A072583 In other words, A000120(k) <> A000120(A000040(k)) and A000120(k) <> A023416(A000040(k)) and A023416(k) <> A000120(A000040(k)) and A023416(k) <> A023416(A000040(k)).
%C A072583 A000120(k) <> A014499(k) and A000120(k) <> A035103(k) and A023416(k) <> A014499(k) and A023416(k) <> A035103(k).
%H A072583 Amiram Eldar, <a href="/A072583/b072583.txt">Table of n, a(n) for n = 1..10000</a>
%F A072583 a(n) = A049084(A072584(n)).
%e A072583 k = 40 = '101000', A000040(40) = 173 = '10101101'.
%t A072583 With[{m = 150}, Select[Transpose[{Range[m], Prime[Range[m]]}], Intersection @@ DigitCount[#, 2] == {} &]][[;; , 1]] (* _Amiram Eldar_, Jul 28 2025 *)
%Y A072583 Cf. A000040, A000120, A014499, A023416, A035103, A049084, A071600, A072577, A072578, A072579, A072584.
%K A072583 nonn,base,easy
%O A072583 1,1
%A A072583 _Reinhard Zumkeller_, Jun 23 2002