OFFSET
1,1
COMMENTS
Mod 9 this sequence is 3, 6, 3, 6, 3, 6, ... This shows that this sequence is disjoint from A004207. - N. J. A. Sloane, Oct 15 2013
REFERENCES
D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.
D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.
G. E. Stevens and L. G. Hunsberger, A Result and a Conjecture on Digit Sum Sequences, J. Recreational Math. 27, no. 4 (1995), pp. 285-288.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
FORMULA
a(n) = A062028(a(n-1)) for n > 1. - Reinhard Zumkeller, Oct 14 2013
a(n) - a(n-1) = A084228(n+1). - Robert G. Wilson v, Jun 27 2014
MATHEMATICA
NestList[# + Total[IntegerDigits[#]] &, 3, 51] (* Jayanta Basu, Aug 11 2013 *)
a[1] = 3; a[n_] := a[n] = a[n - 1] + Total@ IntegerDigits@ a[n - 1]; Array[a, 80] (* Robert G. Wilson v, Jun 27 2014 *)
PROG
(Haskell)
a016052 n = a016052_list !! (n-1)
a016052_list = iterate a062028 3 -- Reinhard Zumkeller, Oct 14 2013
(PARI)
a_list(nn) = { my(f(n, i) = n + vecsum(digits(n)), S=vector(nn+1)); S[1]=3; for(k=2, #S, S[k] = fold(f, S[1..k-1])); S[2..#S] } \\ Satish Bysany, Mar 04 2017
(Python)
from itertools import islice
def A016052_gen(): # generator of terms
yield (a:=3)
while True: yield (a:=a+sum(map(int, str(a))))
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved