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 A072577 #15 Jul 28 2025 03:19:29 %S A072577 5,6,20,22,24,28,31,32,34,37,41,42,49,50,67,68,81,82,84,88,89,93,94, %T A072577 138,139,140,141,142,143,147,151,157,165,192,194,198,200,202,206,207, %U A072577 232,236,241,262,265,270,271,284,285,295,301,328,329,332,333,337 %N A072577 Numbers k such that k and the k-th prime have the same number of 0's in their binary representation. %H A072577 Amiram Eldar, <a href="/A072577/b072577.txt">Table of n, a(n) for n = 1..10000</a> %F A072577 A023416(a(n)) = A023416(A072580(n)) = A035103(n). %F A072577 a(n) = A049084(A072580(n)). %e A072577 In binary representation 20 and A000040(20) = 71 have three 0's: 13 = '10100' and 71 = '1000111', therefore 20 is a term. %t A072577 q[k_] := DigitCount[k, 2, 0] == DigitCount[Prime[k], 2, 0]; Select[Range[350], q] (* _Amiram Eldar_, Jul 28 2025 *) %Y A072577 Cf. A023416, A035103, A049084, A071600, A072578, A072579, A072580. %K A072577 nonn,base,easy %O A072577 1,1 %A A072577 _Reinhard Zumkeller_, Jun 23 2002