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%I #53 Feb 10 2024 11:36:27
%S 3,6,12,15,21,24,30,33,39,51,57,69,84,96,111,114,120,123,129,141,147,
%T 159,174,186,201,204,210,213,219,231,237,249,264,276,291,303,309,321,
%U 327,339,354,366,381,393,408,420,426,438,453,465,480,492
%N a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digits.
%C 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
%D D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.
%D D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.
%D 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.
%H Reinhard Zumkeller, <a href="/A016052/b016052.txt">Table of n, a(n) for n = 1..10000</a>
%H D. R. Kaprekar, <a href="/A003052/a003052_2.pdf">The Mathematics of the New Self Numbers</a> [annotated and scanned]
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F a(n) = A062028(a(n-1)) for n > 1. - _Reinhard Zumkeller_, Oct 14 2013
%F a(n) - a(n-1) = A084228(n+1). - _Robert G. Wilson v_, Jun 27 2014
%t NestList[# + Total[IntegerDigits[#]] &, 3, 51] (* _Jayanta Basu_, Aug 11 2013 *)
%t 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 *)
%o (Haskell)
%o a016052 n = a016052_list !! (n-1)
%o a016052_list = iterate a062028 3 -- _Reinhard Zumkeller_, Oct 14 2013
%o (PARI)
%o 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
%Y Cf. A004207, A007618, A006507, A016096, A230107, A230286, A230287, A084228.
%K nonn,base,easy
%O 1,1
%A _Robert G. Wilson v_
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