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 A031286 Additive persistence: number of summations of digits needed to obtain a single digit (the additive digital root). 19
 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 LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 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: A290104 A031280 A134870 * A031276 A305080 A261794 Adjacent sequences:  A031283 A031284 A031285 * A031287 A031288 A031289 KEYWORD nonn,base AUTHOR EXTENSIONS Corrected by Reinhard Zumkeller, Feb 05 2009 STATUS approved

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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.)