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Analog of A121805, but starting with 9.
9

%I #12 Nov 18 2023 11:53:08

%S 9,100,101,112,133,164,206,268,351,364,408,492,517,592,618,705,762,

%T 789,887,966,1027,1098,1179,1270,1271,1282,1303,1334,1375,1426,1487,

%U 1558,1639,1730,1731,1742,1763,1794,1835,1886,1947,2019,2111,2123,2155,2207,2279,2371

%N Analog of A121805, but starting with 9.

%C Contains 19511030 terms, the last being 999999936.

%H Michael De Vlieger, <a href="/A367353/b367353.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 *)

%o (Python)

%o from itertools import islice

%o def agen(start=9): # generator of terms

%o an, y = start, 1

%o while y < 10:

%o yield an

%o an, y = an + 10*(an%10), 1

%o while y < 10:

%o if str(an+y)[0] == str(y):

%o an += y

%o break

%o y += 1

%o print(list(islice(agen(), 50))) # _Michael S. Branicky_, Nov 18 2023

%Y 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.

%Y Cf. A330128, A330129.

%K nonn,base,fini

%O 1,1

%A _N. J. A. Sloane_, Nov 17 2023