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.

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

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