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%I #21 Oct 27 2018 09:53:38
%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 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 Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/aronsf.pdf">Binary mapping of monotonic sequences and the Aronson function</a>
%o (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)} }
%o (PARI) v=binary(sqrt(2))[2]; for(i=1,#v,if(v[i],print1(i,","))) \\ _Ralf Stephan_, Mar 30 2014
%Y Cf. A051006, A092857, A092875.
%K easy,nonn,base
%O 1,1
%A Ferenc Adorjan (fadorjan(AT)freemail.hu)
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