1,2

The variant where the condition of strict monotonicity is dropped (suggested by Paolo Lava; cf. link) is less straightforward to compute.

The sequence could also be encoded in a more compact way by specifying only the indices n where it jumps (a(n) > a(n-1)+1) and the corresponding values a(n), see A154329-A154330.

M. F. Hasler, Table of n, a(n) for n = 1..73

Eric Angelini, An ugly self-describing sequence.

E. Angelini et al., "Ugly digit sum", SeqFan mailing list, Jan 08, 2008

Starting with a(1)=1, the next term a(2)>a(1) cannot be 2,...,9 (else the sum of these digits would be larger): the least possibility not leading to a contradiction is a(2)=10.

Then we can go on with a(3)=11, a(4)=12, but a(5) cannot be 13, the least possibility is a(5)=20.

See the linked web page for more details and sequences A154329-A154330 for terms beyond those given here.

(PARI) /* NB: This code checks only whether there is a contradiction for the given digits (1st arg), it does not ensure minimality. If the 2nd arg is nonzero, it dumps a list of all digits and partial sums. */

check_A154328(S=[1, 10, 11, 12, 20], dump=0)={

local(d=eval(Vec(concat(concat([""], S)))), t=0, ds=vector(#d, i, t+=d[i]));

dump & print(vector(#d, i, Str(i":"d[i]":"ds[i])));

for(i=1, #S, S[i]>#d & break; ds[S[i]]==S[i]|error("wrong at i=", i, ": [S[i], ds[S[i]]]=", [S[i], ds[S[i]]]));

print("no contradiction for terms <= "#d) }

Cf. A155817 [From Paolo P. Lava (ppl(AT)spl.at), Jul 23 2009]

Sequence in context: A109279 A154770 A098395 this_sequence A112654 A102695 A144582

Adjacent sequences: A154325 A154326 A154327 this_sequence A154329 A154330 A154331

nonn,base

Eric Angelini (eric.angelini(AT)kntv.be) and M. F. Hasler (MHasler(AT)univ-ag.fr), Jan 13 2009