A092855 Representation of sqrt(2) - 1 by an infinite sequence.

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

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

Table of n, a(n) for n=1..67.

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

Prog

(PARI) {/* mtinv(x)= /*Returns the inverse binary mapping of x into a monotonic sequence */ local(z, q, v=[], r=[], l); z=frac(x); v=binary(z)[2]; l=matsize(v)[2]; for(i=1, l, if(v[i]==1, r=concat(r, i))); return(r)} }
(PARI) v=binary(sqrt(2))[2]; for(i=1, #v, if(v[i], print1(i, ", "))) \\ Ralf Stephan, Mar 30 2014

Crossrefs

Cf. A051006, A092857, A092875.

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)

Status

approved