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Search: id:A156344
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| A156344 |
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Number of steps to reach a square starting from n and iterating the map: x->x*ceil(sqrt(x))/floor(sqrt(x)) or zero if no square is reached. |
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+0
1
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| 1, 2, 3, 1, 6, 2, 9, 3, 1, 14, 103, 2, 19, 7, 3, 1, 26, 10, 105, 2, 33, 13, 312, 3, 1, 42, 691, 241, 27190, 2, 51, 21, 11, 260, 3, 1, 62, 26, 14, 8, 151, 2, 73, 31, 17, 492, 268, 3, 1, 86, 2535, 869, 315546, 1065, 183, 2, 99, 43, 2226, 15, 350, 294, 3, 1, 114, 50, 1457, 18
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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We conjecture sequence is never zero.
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FORMULA
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a(k^2)=1, a(k*(k+1))=2, a(k*(k+2))=3, and less trivially it appears a(floor(n^2/4)+1)=1+ceil((n-1)^2/2) and then the square reached is (floor(n^2/4)+1)^2.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=n; c=1; while(frac(sqrt(s))>0, s=s*ceil(sqrt(s))/floor(sqrt(s)); c++); c)
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CROSSREFS
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Cf. A002620, A073524
Sequence in context: A137211 A083855 A062565 this_sequence A119440 A165742 A162984
Adjacent sequences: A156341 A156342 A156343 this_sequence A156345 A156346 A156347
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2009
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