A123171 a(1) = 123, a(n) = sum of digits of all previous terms.

123, 6, 12, 15, 21, 24, 30, 33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, 147, 159, 174, 186, 201, 204, 210, 213, 219, 231, 237, 249, 264, 276, 291, 303, 309, 321, 327, 339, 354, 366, 381, 393, 408, 420, 426, 438, 453, 465, 480, 492, 507, 519, 534

Offset: 1

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 02 2006

Keywords

• nonn
• base

Comments

a(1) = 123 a(2) = 1 + 2 + 3 = 6 a(3) = (1 + 2 + 3) + 6 = 12 a(4) = (1 + 2 + 3) + 6 + (1 + 2) = 15 a(5) = (1 + 2 + 3) + 6 + (1 + 2) + (1 + 5) = 21 a(6) = (1 + 2 + 3) + 6 + (1 + 2) + (1 + 5) + (2 + 1) = 24 a(7) = (1 + 2 + 3) + 6 + (1 + 2) + (1 + 5) + (2 + 1) + (2 + 4) = 30 ...

Essentially the same as A016052. - R. J. Mathar, Jun 18 2008

Links

• James C. McMahon, Table of n, a(n) for n = 1..10000
• Sergio Silva, Teste Numerico.

Crossrefs

Cf. A004207.

Programs

Mathematica

s={123};sum=0;Do[sum=sum+Total[IntegerDigits[s[[-1]]]];AppendTo[s,sum],{n,54}];s (* James C. McMahon, Nov 16 2024 *)

PARI

s=0; a=123; print1(a,","); for(n=1,100,dig=eval(Vec(Str(a)));s=s+sum(i=1,length(dig),dig[i]);print1(s,",");a=s)

Formula

a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 123