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A343951 Numbers with decimal expansion (d_1, ..., d_k) such that all the sums d_i + ... + d_j with 1 <= i <= j <= k are distinct. 1
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 81, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence is finite, the last term being a(5562) = 8657913.

All positive terms are zeroless (A052382) and have distinct decimal digits (A010784).

There are 10, 72, 440, 1622, 2502, 906, 10, and 0 terms with 1..8 digits, resp. - Michael S. Branicky, May 05 2021

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..5562

EXAMPLE

Regarding 12458:

- we have the following partial sums of digits:

     i\j|  1  2  3  4  5

     ---+---------------

       1|  1  3  7 12 20

       2|  .  2  6 11 19

       3|  .  .  4  9 17

       4|  .  .  .  5 13

       5|  .  .  .  .  8

- as they are all distinct, 12458 is a term.

PROG

(PARI) is(n) = { my (d=digits(n), s=setbinop((i, j)->vecsum(d[i..j]), [1..#d])); #s==#d*(#d+1)/2 }

(Python)

def ok(n):

  d, sums = str(n), set()

  for i in range(len(d)):

    for j in range(i, len(d)):

      sij = sum(map(int, d[i:j+1]))

      if sij in sums: return False

      else: sums.add(sij)

  return True

print(list(filter(ok, range(83)))) # Michael S. Branicky, May 05 2021

CROSSREFS

Cf. A010784, A052382, A101274.

Sequence in context: A050759 A039274 A102487 * A102234 A174908 A344543

Adjacent sequences:  A343948 A343949 A343950 * A343952 A343953 A343954

KEYWORD

nonn,base,fini,full

AUTHOR

Rémy Sigrist, May 05 2021

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)