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).

2, 3, 5, 7, 13, 16, 17, 18, 19, 22, 23, 26, 27, 30, 31, 32, 33, 34, 35, 36, 39, 40, 41, 43, 44, 45, 46, 49, 50, 53, 56, 61, 65, 67, 68, 71, 73, 74, 75, 76, 77, 79, 80, 84, 87, 88, 90, 91, 94, 95, 97, 98, 99, 101, 103, 105, 108, 110, 112, 114, 115, 116, 117, 118, 120, 123, 124

Offset

1,1

Comments

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

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.

An example for the inverse mapping is A051006.

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Ferenc Adorjan, Binary mapping of monotonic sequences and the Aronson function.

Mathematica

PositionIndex[First[RealDigits[Sqrt[2], 2, 200, -1]]][1] (* Paolo Xausa, Sep 01 2024 *)

Prog

(PARI) v=binary(sqrt(2))[2]; for(i=1, #v, if(v[i], print1(i, ", "))) \\ Ralf Stephan, Mar 30 2014

Crossrefs

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

Sequence in context: A004682 A173105 A024783 * A100111 A092878 A126059

Adjacent sequences: A092852 A092853 A092854 * A092856 A092857 A092858

Keyword

easy,nonn,base

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Extensions

New name from Joerg Arndt, Aug 26 2024

Status

approved