A367353 Analog of A121805, but starting with 9.

9, 100, 101, 112, 133, 164, 206, 268, 351, 364, 408, 492, 517, 592, 618, 705, 762, 789, 887, 966, 1027, 1098, 1179, 1270, 1271, 1282, 1303, 1334, 1375, 1426, 1487, 1558, 1639, 1730, 1731, 1742, 1763, 1794, 1835, 1886, 1947, 2019, 2111, 2123, 2155, 2207, 2279, 2371

Offset: 1

Author

N. J. A. Sloane, Nov 17 2023

Keywords

• nonn
• base
• fini

Comments

Contains 19511030 terms, the last being 999999936.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Comma sequences in base 10, starting with 1, 2, 4, 5, 6, 7, 8, 9, 10 are A121805, A139284, A366492, A367337, A367350, A367351, A367352, A367353, A367354. Starting with 3 is trivial, and those starting with 11, 12, 13 are essentially duplicates.

Cf. A330128, A330129.

Programs

Mathematica

b = 10; m = b - 1; a[1] = 9; a[n_] := a[n] = For[r = Mod[a[n - 1], b]; y = 0, y <= m, y++, If[y == IntegerDigits[#, b][[1]], Return[#]] &[a[n - 1] + b r + y]]; Array[a, 45] (* Michael De Vlieger, Nov 18 2023, after Jean-François Alcover at A121805 *)

Python

from itertools import islice
def agen(start=9): # generator of terms
    an, y = start, 1
    while y < 10:
        yield an
        an, y = an + 10*(an%10), 1
        while y < 10:
            if str(an+y)[0] == str(y):
                an += y
                break
            y += 1
print(list(islice(agen(), 50))) # Michael S. Branicky, Nov 18 2023