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A366197 Lexicographically earliest permutation of the nonnegative integers such that the absolute difference between the digitsum of a(n) and the digitsum of a(n+2) = 1.

%I A366197 #22 Oct 23 2023 02:23:04
%S A366197 0,1,10,2,11,3,12,4,13,5,14,6,15,7,16,8,17,9,18,19,26,27,25,28,24,29,
%T A366197 23,37,22,36,21,35,20,34,30,33,31,32,41,40,42,50,43,51,44,52,45,53,46,
%U A366197 54,38,55,39,47,49,48,57,56,58,64,59,63,67,62,66,61,65,60
%N A366197 Lexicographically earliest permutation of the nonnegative integers such that the absolute difference between the digitsum of a(n) and the digitsum of a(n+2) = 1.
%H A366197 John Tyler Rascoe, <a href="/A366197/b366197.txt">Table of n, a(n) for n = 0..10000</a>
%e A366197 DS stands hereunder for DigitSum:
%e A366197 a(0) =  0 (DS 0) and a(2) = 10 (DS 1) and the absolute difference 0 - 1 = 1;
%e A366197 a(1) =  1 (DS 1) and a(3) =  2 (DS 2) and the absolute difference 1 - 2 = 1;
%e A366197 a(2) = 10 (DS 1) and a(4) = 11 (DS 2) and the absolute difference 1 - 2 = 1;
%e A366197 a(3) =  2 (DS 2) and a(5) =  3 (DS 3) and the absolute difference 2 - 3 = 1;
%e A366197 a(4) = 11 (DS 2) and a(6) = 12 (DS 3) and the absolute difference 2 - 3 = 1; etc.
%o A366197 (Python)
%o A366197 from itertools import count, filterfalse
%o A366197 def DS(y):
%o A366197     z = str(y)
%o A366197     return sum(int(z[i]) for i in range (0,len(z)))
%o A366197 def A366197_list(n_max):
%o A366197     A = [0,1]
%o A366197     S = set(A)
%o A366197     for n in range(2,n_max+1):
%o A366197         for i in filterfalse(S.__contains__, count(1)):
%o A366197             if abs(DS(A[n-2])-DS(i)) == 1:
%o A366197                 A.append(i)
%o A366197                 S.add(i)
%o A366197                 break
%o A366197     return(A) # _John Tyler Rascoe_, Oct 22 2023
%Y A366197 Cf. A007953, A108971, A318486.
%K A366197 base,nonn
%O A366197 0,3
%A A366197 _Eric Angelini_, Oct 03 2023
%E A366197 More terms from _Alois P. Heinz_, Oct 03 2023