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Search: id:A092855
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| A092855 |
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Representation of sqrt(2)-1 by an infinite sequence. |
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+0
18
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 reach in primes, but cf. A092875.
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LINKS
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Ferenc Adorjan, Binary mapping of monotonic sequences and the Aronson function
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PROGRAM
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(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)} }
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CROSSREFS
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Cf. A051006, A092857, A092858, A092859, A092860, A092861, A092862, A092863, A092874.
Sequence in context: A031344 A004682 A024783 this_sequence A100111 A092878 A126059
Adjacent sequences: A092852 A092853 A092854 this_sequence A092856 A092857 A092858
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KEYWORD
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easy,nonn
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AUTHOR
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Ferenc Adorjan (fadorjan(AT)freemail.hu)
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