A375758 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the initial digit of n divides a(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 21, 27, 33, 39, 42, 45, 48, 51, 54, 57, 40, 44, 52, 56, 60, 64, 68, 72, 76, 80, 25, 35, 50, 55, 65, 70, 75, 85, 90, 95, 66, 78, 84, 96, 102, 108, 114

Offset

1,2

Comments

This sequence is a permutation of the positive integers with inverse A375759.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms are:
  n   a(n)  a(n)/A30(n)  |  n   a(n)  a(n)/A30(n)
  --  ----  -----------  |  --  ----  -----------
   1     1            1  |  16    16           16
   2     2            1  |  17    17           17
   3     3            1  |  18    18           18
   4     4            1  |  19    19           19
   5     5            1  |  20    20           10
   6     6            1  |  21    22           11
   7     7            1  |  22    24           12
   8     8            1  |  23    26           13
   9     9            1  |  24    28           14
  10    10           10  |  25    30           15
  11    11           11  |  26    32           16
  12    12           12  |  27    34           17
  13    13           13  |  28    36           18
  14    14           14  |  29    38           19
  15    15           15  |  30    21            7

Prog

(PARI) \\ See Links section.
(Python)
from itertools import count, islice
def agen(): # generator of terms
    aset, m = set(), 1
    for n in count(1):
        n1 = int(str(n)[0])
        an = next(k for k in count(m) if k not in aset and k%n1 == 0)
        yield an
        aset.add(an)
        while m in aset: m += 1
print(list(islice(agen(), 67))) # Michael S. Branicky, Jan 27 2025

Crossrefs

Cf. A000030, A308539, A375759 (inverse).

Sequence in context: A324720 A374847 A247756 * A032520 A034837 A096105

Adjacent sequences: A375755 A375756 A375757 * A375759 A375760 A375761

Keyword

nonn,base

Author

Rémy Sigrist, Aug 26 2024

Status

approved