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Search: id:A005184
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| A005184 |
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Self-contained numbers: odd numbers n whose Collatz sequence contains a higher multiple of n.
(Formerly M5220)
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+0
4
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OFFSET
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1,1
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COMMENT
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Collatz: a[n+1] = a[n]/2 if a[n] is even, 3*a[n]+1 if a[n] is odd.
No others less than 250000000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 07 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. K. Guy, Unsolved Problems in Number Theory, E16.
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EXAMPLE
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The Collatz sequence of 31 is 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310 ... 310 is a multiple of 31, so the number 31 is "self-contained".
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MATHEMATICA
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isValid[n_] := Module[{d}, d = n; While[d != 1, If[EvenQ[d], d = d/2, d = 3*d + 1]; If[IntegerQ[d/n], Return[True]]]; Return[False]]; For[n = 1, n <= 250000000, n += 2, If[isValid[n], Print[n]]]; - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 07 2006
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PROGRAM
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(PARI) m=5; d=2; while(1, n=(3*m+1)\2; until(n==1, n=if(n%2, 3*n+1, n\2); if(n%m==0, print(m, " ", n); break)); m+=d; d=6-d)
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CROSSREFS
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The ratios "higher multiple of n" / n are given in A059198.
Sequence in context: A044550 A055810 A142522 this_sequence A096731 A039518 A142715
Adjacent sequences: A005181 A005182 A005183 this_sequence A005185 A005186 A005187
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com)
Better description from Jack Brennen, Feb 07 2003.
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