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A064702
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Nonnegative numbers such that additive and multiplicative digital roots coincide.
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5
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0, 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
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OFFSET
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1,3
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COMMENTS
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If k is in this sequence then all permutations of (the digits of) k are in this sequence.
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LINKS
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MAPLE
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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
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okQ[n_]:=NestWhile[Times@@IntegerDigits[#]&, n, #>9&]== NestWhile[ Total[ IntegerDigits[ #]]&, n, #>9&]; Select[Range[1000], okQ] (* Harvey P. Dale, Apr 20 2011 *)
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PROG
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(Haskell)
a064702 n = a064702_list !! (n-1)
a064702_list = filter (\x -> a010888 x == a031347 x) [1..]
(PARI) is(n) = my(cn = n); while(cn > 9, d = digits(cn); cn = prod(i = 1, #d, d[i])); cn - 1 == (n-1)%9 \\ David A. Corneth, Aug 23 2018
(Python)
from math import prod
while n > 9: n = sum(map(int, str(n)))
return n
while n > 9: n = prod(map(int, str(n)))
return n
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CROSSREFS
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KEYWORD
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easy,nice,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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