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 A092855 #47 Sep 02 2024 08:37:55
%S A092855 2,3,5,7,13,16,17,18,19,22,23,26,27,30,31,32,33,34,35,36,39,40,41,43,
%T A092855 44,45,46,49,50,53,56,61,65,67,68,71,73,74,75,76,77,79,80,84,87,88,90,
%U A092855 91,94,95,97,98,99,101,103,105,108,110,112,114,115,116,117,118,120,123,124
%N A092855 Numbers k such that the k-th bit in the binary expansion of sqrt(2) - 1 is 1: sqrt(2) - 1 = Sum_{n>=1} 1/2^a(n).
%C A092855 Previous name was: Representation of sqrt(2) - 1 by an infinite sequence.
%C A092855 Any real number in the range (0,1), having infinite number of nonzero binary digits, can be represented by a monotonic infinite sequence, such a way that n is in the sequence iff the n-th digit in the fraction part of the number is 1. See also A092857.
%C A092855 An example for the inverse mapping is A051006.
%C A092855 It is relatively rich in primes, but cf. A092875.
%H A092855 Paolo Xausa, <a href="/A092855/b092855.txt">Table of n, a(n) for n = 1..10000</a>
%H A092855 Ferenc Adorjan, <a href="https://www.academia.edu/104976035/Binary_Mapping_of_Monotonic_Sequences_the_Aronson_and_the_Cellular_Automaton_Functions">Binary mapping of monotonic sequences and the Aronson function</a>.
%t A092855 PositionIndex[First[RealDigits[Sqrt[2], 2, 200, -1]]][1] (* _Paolo Xausa_, Sep 01 2024 *)
%o A092855 (PARI) v=binary(sqrt(2))[2]; for(i=1,#v,if(v[i],print1(i,","))) \\ _Ralf Stephan_, Mar 30 2014
%Y A092855 Cf. A004539, A051006, A092857, A092875, A320985 (complement).
%K A092855 easy,nonn,base
%O A092855 1,1
%A A092855 Ferenc Adorjan (fadorjan(AT)freemail.hu)
%E A092855 New name from _Joerg Arndt_, Aug 26 2024