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A362335 Lexicographically earliest sequence of distinct nonnegative terms wherein every digit of a(n) is the absolute difference of two adjacent digits in a(n+1).

%I A362335 #44 May 28 2023 11:34:13
%S A362335 0,11,10,100,110,112,102,1002,1022,1102,1120,1124,1026,10028,10086,
%T A362335 10082,10866,10822,10886,10882,11086,11082,11208,11976,10928,100913,
%U A362335 10096,10093,10966,10933,10996,10993,11096,11093,22309,11309,23009,13009,23099,13099,23309
%N A362335 Lexicographically earliest sequence of distinct nonnegative terms wherein every digit of a(n) is the absolute difference of two adjacent digits in a(n+1).
%C A362335 All terms > a(24) contain at least one 9 with an adjacent 0. All terms > a(25) contain at least one instance of identical adjacent digits.
%H A362335 Michael S. Branicky, <a href="/A362335/b362335.txt">Table of n, a(n) for n = 1..10000</a>
%e A362335 a(125) = 9902. The next term is 10097, not 20009, because, in spite of its providing more digit differences than are needed, it is lexicographically earlier.
%o A362335 (Python)
%o A362335 from itertools import count, islice
%o A362335 def c(k, d):
%o A362335     dk = list(map(int, str(k)))
%o A362335     return set(abs(dk[i+1]-dk[i]) for i in range(len(dk)-1)) >= d
%o A362335 def agen(): # generator of terms
%o A362335     an, aset = 0, {0}
%o A362335     while True:
%o A362335         yield an
%o A362335         d = set(map(int, set(str(an))))
%o A362335         an = next(k for k in count(10**len(d)) if k not in aset and c(k, d))
%o A362335         aset.add(an)
%o A362335 print(list(islice(agen(), 41))) # _Michael S. Branicky_, May 27 2023
%o A362335 def A362335(n, A=[0]):
%o A362335     while len(A) <= n:
%o A362335         z = lambda a: zip(d := tuple(int(d) for d in str(a)), d[1:])
%o A362335         D = set(str(A[-1])) ; a = 10**len(D)
%o A362335         while a in A or D - set(str(abs(x-y)) for x,y in z(a)): a += 1
%o A362335         A . append(a)
%o A362335     return A[n] # _M. F. Hasler_, May 27 2023
%o A362335 (PARI) {upto(N) = my(U=[], a=0); vector(N,n, if(n>1, my(da=Set(if(a,digits(a)))); a=10^#da; while( setsearch(U,a) || #setminus(da, Set(abs((n=digits(a))[^1]-n[^-1]))), a++)); U=setunion(U,[a]); a)} \\ _M. F. Hasler_, May 27 2023
%K A362335 nonn,base
%O A362335 1,2
%A A362335 _Eric Angelini_ and _Hans Havermann_, May 27 2023
%E A362335 a(27) and beyond from _Michael S. Branicky_, May 27 2023