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Analog of A121805, but starting with 7.
9

%I #9 Nov 18 2023 11:54:48

%S 7,85,136,197,269,362,385,439,534,579,675,732,759,857,936

%N Analog of A121805, but starting with 7.

%t b = 10; m = b - 1; a[1] = 7; 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]]; TakeWhile[Array[a, 45], IntegerQ] (* _Michael De Vlieger_, Nov 18 2023, after _Jean-François Alcover_ at A121805 *)

%o (Python)

%o def agen(start=7): # 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(agen())) # _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,fini,full,base

%O 1,1

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