A359356 a(n-1) + a(n) has only digits also in a(n); lexicographically earliest such sequence of distinct nonnegative integers.

0, 1, 10, 12, 179, 132, 1048, 416, 135, 126, 125, 1025, 136, 15, 146, 82, 31, 302, 53, 128, 183, 130, 14, 157, 1254, 139, 304, 73, 41, 403, 74, 208, 103, 152, 1028, 91, 21, 201, 32, 159, 506, 160, 17, 124, 1036, 104, 51, 504, 95, 16, 204, 62, 129, 203, 52, 503

Offset

0,3

Comments

Conjectured to be a permutation of the nonnegative integers.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Eric Angelini, A last pair sum linked to an alphabet, [math-fun] list, Dec. 26, 2022.

Example

The sequence of pairwise sums a(n-1) + a(n), n > 0, is (1, 11, 22, 191, 311, 1180, 1464, 551, 261, 251, 1150, 1161, 151, 161, 228, 113, 333, 355, 181, 311, ...)
After the smallest possible choice a(0) = 0, a(1) = 1 has the same digits as a(0) + a(1).
Then, a(2) = 10 is the smallest yet unused nonnegative integer such that a(1) + a(2) = 11 has all its digits also occurring in a(2). (The number 0 is excluded since it appeared earlier as a(0).)
Then, a(3) = 12 is the smallest yet unused nonnegative integer such that a(2) + a(3) = 22 has all its digits also occurring in a(3). (The smaller solutions 0 and 1 are again excluded since they appeared earlier.)

Maple

b:= proc() false end:
d:= proc(n) option remember; {convert(n, base, 10)[]} end:
a:= proc(n) option remember; local k; for k
      while b(k) or d(a(n-1)+k) minus d(k)<>{} do od:
      b(k):= true; k
    end: a(0):=0:
seq(a(n), n=0..55);  # Alois P. Heinz, Jan 03 2023

Prog

(Python)
def A359356(n, A=[0]):
  while len(A) <= n:
    t = 0
    while t in A or any(d not in str(t) for d in str(t+A[-1])):
      t += 1
    A.append(t)
  return A[n]

Crossrefs

Cf. A359517 (conjectured inverse permutation).

Sequence in context: A155005 A219213 A078217 * A178639 A087392 A255534

Adjacent sequences: A359353 A359354 A359355 * A359357 A359358 A359359

Keyword

nonn,base

Author

M. F. Hasler and Eric Angelini, Dec 27 2022

Status

approved