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Search: id:A105690
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| A105690 |
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A simple "Fractal Jump Sequence" (FJS). A FJS is a sequence of digits embedding an infinite amount of copies of itself. Modus operandi: underline the first digit "a" of such a sequence then jump over the next "a" digits and underline the digit "b" on which you land. Jump now from there over the next "b" digits and underline the digit "c" on which you land. Etc. The "abc...n..." succession of underlined digits is the sequence itself. |
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| 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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This is how to construct the sequence: start with 2 on rows a and b; put 2 empty spaces behind the 2 on row a; choose any two digits and put them on row b under the 2 empty spaces of row a; go back to row a and add the same two digits but each one with its according spaces (1 must always be followed by 1 space on row a and 2 must always be followed by 2 spaces); go back to row b and add under the next available spaces of a the digits necessary so to have the same succession of digits in rows b and a. The sequence builds itself automatically. The row (c) is obtained by "pushing" (a) into (b) -- [the first digit of a and b melt in a single copy of themselves]. Row (c) is the FJS sequence above.
(a)..2..1.2..1.1.2..1.2..1.1.1.2..2.....
(b)..212.1.12.1.2.11.1.22.1.1.1.12.22...
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(c)..21211212111221111222111111212222...
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EXAMPLE
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To build such sequences one has only to choose the first digit d and the d digits to put under the d spaces of row (a).
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CROSSREFS
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Sequence in context: A096860 A128185 A022300 this_sequence A006337 A006338 A020903
Adjacent sequences: A105687 A105688 A105689 this_sequence A105691 A105692 A105693
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KEYWORD
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base,easy,nonn
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AUTHOR
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Eric Angelini (eric.angelini(AT)kntv.be), May 04 2005
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