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

Author

Rémy Sigrist, Aug 26 2024

Keywords

• nonn
• base

Comments

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

Examples

			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
		

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

Crossrefs

Cf. A000030, A308539, A375759 (inverse).

Programs

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