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

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

• easy
• nonn
• base

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

Extensions

New name from Joerg Arndt, Aug 26 2024