A337159 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, A033307(n + a(n)) = A033307(n).

0, 13, 14, 15, 16, 17, 18, 19, 20, 2, 40, 1, 3, 4, 21, 6, 33, 8, 51, 53, 60, 11, 80, 9, 100, 7, 120, 5, 140, 10, 160, 12, 157, 41, 163, 39, 23, 37, 31, 35, 49, 73, 67, 71, 85, 29, 103, 27, 121, 47, 141, 25, 137, 43, 143, 61, 144, 59, 145, 57, 45, 55, 63, 93

Offset

0,2

Comments

This sequence is a permutation of the nonnegative integers: repunits induce runs of consecutive equal terms of arbitrary size in A033307, thus allowing any value to eventually occur.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Scatterplot of the first 10000 terms

Rémy Sigrist, PARI program for A337159

Index entries for sequences that are permutations of the natural numbers

Prog

(PARI) See Links section.
(Python)
def aupton(terms):
  alst, A033307, last, used, n, an = [], '1', 1, set(), 0, 0
  while n <= terms:
    while an in used: an += 1
    while len(A033307) <= n + an: last += 1; A033307 += str(last)
    if A033307[n + an] == A033307[n]:
      alst += [an]; used.add(an); n += 1; an = 0
    else: an += 1
  return alst
print(aupton(63)) # Michael S. Branicky, Jan 30 2021

Crossrefs

Cf. A033307, A340490.

Sequence in context: A196461 A004502 A020512 * A297275 A296745 A178402

Adjacent sequences: A337156 A337157 A337158 * A337160 A337161 A337162

Keyword

nonn,look,base

Author

Rémy Sigrist, Jan 30 2021

Status

approved