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A031286
Additive persistence: number of summations of digits needed to obtain a single digit (the additive digital root).
20
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
OFFSET
0,20
LINKS
Antonios Meimaris, On the additive persistence of a number in base p, Preprint, 2015.
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Additive Persistence
MAPLE
read("transforms") ;
A031286 := proc(n)
local a, nper;
nper := n ;
a := 0 ;
while nper > 9 do
nper := digsum(nper) ;
a := a+1 ;
end do:
a ;
end proc:
seq(A031286(n), n=0..80) ; # R. J. Mathar, Jan 02 2018
MATHEMATICA
lst = {}; Do[s = 0; While[n > 9, s++; n = Plus @@ IntegerDigits[n]]; AppendTo[lst, s], {n, 0, 98}]; lst (* Arkadiusz Wesolowski, Oct 17 2012 *)
PROG
(PARI) dsum(n)=my(s); while(n, s+=n%10; n\=10); s
a(n)=my(s); while(n>9, s++; n=dsum(n)); s \\ Charles R Greathouse IV, Sep 13 2012
(Python)
def A031286(n):
ap = 0
while n > 9:
n = sum(int(d) for d in str(n))
ap += 1
return ap
# Chai Wah Wu, Aug 23 2014
CROSSREFS
Cf. A010888 (additive digital root of n).
Cf. A031347 (multiplicative digital root of n).
Cf. A031346 (multiplicative persistence of n).
Cf. also A006050, A045646.
Cf. Numbers with additive persistence k: A304366 (k=1), A304367 (k=2), A304368 (k=3), A304373 (k=4). - Jaroslav Krizek, May 28 2018
Sequence in context: A308479 A031280 A134870 * A031276 A305080 A261794
KEYWORD
nonn,base
EXTENSIONS
Corrected by Reinhard Zumkeller, Feb 05 2009
STATUS
approved