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A375460 Lexicographically earliest sequence of distinct nonnegative terms arranged in successive chunks whose digitsum = 10.

%I A375460 #22 Aug 16 2024 21:09:10
%S A375460 0,1,2,3,4,5,10,11,20,6,12,100,7,21,8,101,9,1000,13,14,10000,15,22,16,
%T A375460 30,17,110,18,100000,19,23,31,1000000,24,40,25,102,26,200,27,10000000,
%U A375460 28,32,41,33,103,34,111,35,1001,36,100000000,37,42,112,43,120,44,1010,45,1000000000
%N A375460 Lexicographically earliest sequence of distinct nonnegative terms arranged in successive chunks whose digitsum = 10.
%C A375460 The first integer that will never appear in the sequence is 29, as its digitsum exceeds 10.
%C A375460 From _Michael S. Branicky_, Aug 16 2024: (Start)
%C A375460 Infinite since A052224 is infinite (as are all sequences with digital sum 1..10).
%C A375460 a(6492) has 1001 digits. (End)
%H A375460 Michael S. Branicky, <a href="/A375460/b375460.txt">Table of n, a(n) for n = 1..6491</a>
%e A375460 The first chunk of integers with digitsum 10 is (0,1,2,3,4);
%e A375460 the next one is (5,10,11,20),
%e A375460 the next one is (6,12,100),
%e A375460 the next one is (7,21),
%e A375460 the next one is (8,101),
%e A375460 the next one is (9,1000),
%e A375460 the next one is (13,14,10000), etc.
%e A375460 The concatenation of the above chunks produce the sequence.
%o A375460 (Python)
%o A375460 from itertools import islice
%o A375460 def bgen(ds): # generator of terms with digital sum ds
%o A375460     def A051885(n): return ((n%9)+1)*10**(n//9)-1 # due to Chai Wah Wu
%o A375460     def A228915(n): # due to M. F. Hasler
%o A375460         p = r = 0
%o A375460         while True:
%o A375460             d = n % 10
%o A375460             if d < 9 and r: return (n+1)*10**p + A051885(r-1)
%o A375460             n //= 10; r += d; p += 1
%o A375460     k = A051885(ds)
%o A375460     while True: yield k; k = A228915(k)
%o A375460 def agen(): # generator of terms
%o A375460     an, ds_block = 0, 0
%o A375460     dsg = [None] + [bgen(i) for i in range(1, 11)]
%o A375460     dsi = [None] + [(next(dsg[i]), i) for i in range(1, 11)]
%o A375460     while True:
%o A375460         yield an
%o A375460         an, ds_an = min(dsi[j] for j in range(1, 11-ds_block))
%o A375460         ds_block = (ds_block + ds_an)%10
%o A375460         dsi[ds_an] = (next(dsg[ds_an]), ds_an)
%o A375460 print(list(islice(agen(), 61))) # _Michael S. Branicky_, Aug 16 2024
%Y A375460 Cf. A166311, A051885, A228915.
%Y A375460 Numbers with digital sum 1..10: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10).
%K A375460 base,nonn
%O A375460 1,3
%A A375460 _Eric Angelini_, Aug 15 2024
%E A375460 a(46) and beyond from _Michael S. Branicky_, Aug 16 2024.