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A064702
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Numbers n such that a(n)=m(n) where a(n) is the (additive) digital root of n and m(n) is the multiplicative digital root of n.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 123, 132, 137, 139, 168, 173, 179, 186, 188, 193, 197, 213, 231, 233, 267, 276, 299, 312, 317, 319, 321, 323, 332, 346, 364, 371, 389, 391, 398, 436, 463, 618, 627, 634, 643, 672, 681, 713, 719, 726, 731, 762, 791, 816, 818, 839
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If k is in this sequence then all permutations of k are in this sequence.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
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MAPLE
| A007954 := proc(n) return mul(d, d=convert(n, base, 10)): end: A031347 := proc(n) local m: m:=n: while(length(m)>1)do m:=A007954(m): od: return m: end: A064702 := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(A031347(k)-1 = (k-1) mod 9)then return k: fi: od: end: seq(A064702(n), n=1..56); # Nathaniel Johnston, May 04 2011
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MATHEMATICA
| okQ[n_]:=NestWhile[Times@@IntegerDigits[#]&, n, #>9&]== NestWhile[Total[IntegerDigits[#]]&, n, #>9&]; Select[Range[1000], okQ] (* From Harvey P. Dale, Apr 20 2011 *)
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CROSSREFS
| Cf. A031347, A010888.
Sequence in context: A128290 A110002 A064158 * A034710 A061672 A132080
Adjacent sequences: A064699 A064700 A064701 * A064703 A064704 A064705
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KEYWORD
| easy,nice,nonn,base
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AUTHOR
| Santi Spadaro (spados(AT)katamail.com), Oct 12 2001
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