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 A377815 #21 Nov 17 2024 07:35:12 %S A377815 1,5,2,3,4,8,15,255,7,11,13,14,16,19,21,22,6,25,32,9,26,63,65535,23, %T A377815 28,10,12,64,17,95,111,128,27,256,4294967295,29,35,18,20,37,38,41,42, %U A377815 44,49,50,52,56,67,69,24,70,73,512,30,33,31,39,18446744073709551615 %N A377815 Lexicographically earliest infinite sequence of distinct positive integers such that the binary concatenation of its terms yields the same string as the binary concatenation of the binary weights of its terms. %C A377815 The sequence makes huge jumps. For example, here are three consecutive terms: a(70) = 88, a(71) = 2^256-1, a(72) = 97. %C A377815 Runs of 0 bits induce large terms since z consecutive 0 bits becomes a term with weight at least 2^z and the smallest such is 2^(2^z) - 1. %C A377815 The base-2 analog of A302656. The first b terms of this sequence's base-b analog are 1,2,...,(b-1), followed by (b^2+b-1). %H A377815 Dominic McCarty, <a href="/A377815/b377815.txt">Table of n, a(n) for n = 1..451</a> %H A377815 Dominic McCarty, <a href="/A377815/a377815.png">Log log scatterplot of (n, a(n)) for 1 < n <= 10000</a> %H A377815 Dominic McCarty, <a href="/A377815/a377815_1.txt">Table of n, a(n), binary weight of a(n) for n = 1..100000</a> %e A377815 (a(n)): %e A377815 1, 5, 2, 3, 4, 8, 15, 255, 7, ... %e A377815 (a(n)) in binary: %e A377815 1, 101, 10, 11, 100, 1000, 1111, 11111111, 111, ... %e A377815 Binary weights of (a(n)): %e A377815 1, 2, 1, 2, 1, 1, 4, 8, 3, ... %e A377815 Binary weights of (a(n)) in binary: %e A377815 1, 10, 1, 10, 1, 1, 100, 1000, 11, ... %e A377815 The two binary lines are the same when concatenated. %Y A377815 Cf. A302656 %K A377815 nonn,base %O A377815 1,2 %A A377815 _Dominic McCarty_, Nov 08 2024