A092855 - OEIS

%I #47 Sep 02 2024 08:37:55

%S 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 44,45,46,49,50,53,56,61,65,67,68,71,73,74,75,76,77,79,80,84,87,88,90,

%U 91,94,95,97,98,99,101,103,105,108,110,112,114,115,116,117,118,120,123,124

%N 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 Previous name was: Representation of sqrt(2) - 1 by an infinite sequence.

%C 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 An example for the inverse mapping is A051006.

%C It is relatively rich in primes, but cf. A092875.

%H Paolo Xausa, <a href="/A092855/b092855.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 PositionIndex[First[RealDigits[Sqrt[2], 2, 200, -1]]][1] (* _Paolo Xausa_, Sep 01 2024 *)

%o (PARI) v=binary(sqrt(2))[2]; for(i=1,#v,if(v[i],print1(i,","))) \\ _Ralf Stephan_, Mar 30 2014

%Y Cf. A004539, A051006, A092857, A092875, A320985 (complement).

%K easy,nonn,base

%O 1,1

%A Ferenc Adorjan (fadorjan(AT)freemail.hu)

%E New name from _Joerg Arndt_, Aug 26 2024