A154328 Lexicographically earliest strictly increasing sequence having the property that a(n) is the sum of the first a(n) digits of the sequence.

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

Offset

1,2

Comments

The variant where the condition of strict monotonicity is dropped 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.

Links

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

Example

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.

Prog

(PARI) /* Note: 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) }

Crossrefs

Cf. A155817.

Sequence in context: A098395 A207968 A207671 * A112654 A362987 A235828

Adjacent sequences: A154325 A154326 A154327 * A154329 A154330 A154331

Keyword

nonn,base

Author

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

Status

approved