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A031286
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Additive persistence: number of summations of digits needed to obtain a single digit (the additive digital root).
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20
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,20
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LINKS
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MAPLE
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read("transforms") ;
local a, nper;
nper := n ;
a := 0 ;
while nper > 9 do
nper := digsum(nper) ;
a := a+1 ;
end do:
a ;
end proc:
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MATHEMATICA
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lst = {}; Do[s = 0; While[n > 9, s++; n = Plus @@ IntegerDigits[n]]; AppendTo[lst, s], {n, 0, 98}]; lst (* Arkadiusz Wesolowski, Oct 17 2012 *)
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PROG
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(PARI) dsum(n)=my(s); while(n, s+=n%10; n\=10); s
(Python)
ap = 0
while n > 9:
n = sum(int(d) for d in str(n))
ap += 1
return ap
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CROSSREFS
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Cf. A010888 (additive digital root of n).
Cf. A031347 (multiplicative digital root of n).
Cf. A031346 (multiplicative persistence of n).
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KEYWORD
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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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