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 A385157 #43 Jun 27 2025 04:14:04 %S A385157 1,2,3,9,27,65,95,123,163,303,451,597,760,1757,2546,2700,7142,25030, %T A385157 25719,25772,49105,61426,90981,107497,194210,659077,6732590,8513462, %U A385157 9344030,14549893,32276115,89912342,181720904,280120681,437484689,896754175,10625891495,30605576222 %N A385157 Numbers k so that the binary expansion of 3^k starts with the binary expansion of k. %e A385157 9 is in the sequence as 3^9 is 100110011100011 in binary, and 9 is 1001. %t A385157 q[k_] := k < Log[3, k+1] + (Floor[k*Log2[3]-Log2[k]])/Log2[3]; Select[Range[10^5], q] (* _Amiram Eldar_, Jun 20 2025 *) %o A385157 (PARI) isok(k) = my(bk = binary(k), vb=Vec(binary(3^k), #bk)); vb == bk; \\ _Michel Marcus_, Jun 20 2025 %Y A385157 Cf. A000244, A004656. %K A385157 nonn,base %O A385157 1,2 %A A385157 _Jayde S. Massmann_, Jun 19 2025 %E A385157 a(26) from _Hugo Pfoertner_, Jun 20 2025 %E A385157 a(27)-a(36) from _Amiram Eldar_, Jun 20 2025 %E A385157 a(37)-a(38) from _Jinyuan Wang_, Jun 27 2025