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A154328 Lexicographically earliest strictly increasing sequence having the property that a(n) is the sum of the first a(n) digits of the sequence. 4
1, 10, 11, 12, 20, 111, 112, 120, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 10000, 10000000000000000000, 10000000800000000000, 10000000800000000001, 10000000800000000002 (list; graph; refs; listen; history; text; internal format)



The variant where the condition of strict monotonicity is dropped (suggested by Paolo P. 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, An ugly self-describing sequence [Cached copy, with permission]

E. Angelini et al., "Ugly digit sum", SeqFan mailing list, Jan 08 2009


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.

Sequence in context: A098395 A207968 A207671 * A112654 A235828 A102695

Adjacent sequences:  A154325 A154326 A154327 * A154329 A154330 A154331




Eric Angelini and M. F. Hasler, Jan 13 2009



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Last modified July 21 12:45 EDT 2017. Contains 289642 sequences.