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A031286 Additive persistence: number of summations of digits needed to obtain a single digit (the additive digital root). 12
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)
OFFSET

0,20

REFERENCES

Meimaris Antonios, On the additive persistence of a number in base p, Preprint, 2015.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Eric Weisstein's World of Mathematics, Additive Persistence

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.

Sequence in context: A290104 A031280 A134870 * A031276 A261794 A098744

Adjacent sequences:  A031283 A031284 A031285 * A031287 A031288 A031289

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

EXTENSIONS

Corrected by Reinhard Zumkeller, Feb 05 2009

STATUS

approved

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Last modified November 23 00:33 EST 2017. Contains 295107 sequences.