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A374504 Lexicographically earliest sequence of distinct nonnegative terms such that the absolute difference between the rightmost digit of a(n) and the leftmost digit of a(n+1) is the largest possible one.

%I A374504 #13 Jul 19 2024 19:25:34
%S A374504 0,9,1,90,91,92,93,94,95,10,96,11,97,12,98,13,99,14,900,901,902,903,
%T A374504 904,905,15,16,17,18,19,100,906,101,907,102,908,103,909,104,910,911,
%U A374504 912,913,914,915,105,106,107,108,109,110,916,111,917,112,918,113,919,114,920,921,922,923,924,925,115,116,117,118,119
%N A374504 Lexicographically earliest sequence of distinct nonnegative terms such that the absolute difference between the rightmost digit of a(n) and the leftmost digit of a(n+1) is the largest possible one.
%C A374504 Only numbers starting with 1 or 9 are in the sequence, except for a(1).
%C A374504 The first 9 absolute differences are 9,8,8,9,8,7,6,5,4. The next 20 absolute differences form a pattern that repeats itself forever: 9,5,8,6,7,7,6,8,5,9,8,7,6,5,4,4,5,6,7,8.
%H A374504 Michael S. Branicky, <a href="/A374504/b374504.txt">Table of n, a(n) for n = 1..10000</a>
%e A374504 The digits touching the 1st comma (0 and 9) have an absolute difference of 9;
%e A374504 The digits touching the 2nd comma (9 and 1) have an absolute difference of 8;
%e A374504 The digits touching the 3rd comma (1 and 9) have an absolute difference of 8;
%e A374504 The digits touching the 4th comma (0 and 9) have an absolute difference of 9;
%e A374504 The digits touching the 5th comma (1 and 9) have an absolute difference of 8;
%e A374504 The digits touching the 6th comma (2 and 9) have an absolute difference of 7;
%e A374504 The digits touching the 7th comma (3 and 9) have an absolute difference of 6;
%e A374504 The digits touching the 8th comma (4 and 9) have an absolute difference of 5;
%e A374504 The digits touching the 9th comma (5 and 1) have an absolute difference of 4; from now on, the absolute differences enter into a loop.
%o A374504 (Python)
%o A374504 from itertools import islice
%o A374504 def gen(d): # generator of terms that start with d
%o A374504     pow10 = 1
%o A374504     while True:
%o A374504         for i in range(d*pow10, (d+1)*pow10):
%o A374504             yield i
%o A374504         pow10 *= 10
%o A374504 def agen(): # generator of terms
%o A374504     an, g1, g9 = 0, gen(1), gen(9)
%o A374504     next1, next9 = next(g1), next(g9)
%o A374504     while True:
%o A374504         yield an
%o A374504         rightmost = an%10
%o A374504         if rightmost > 5 or (rightmost == 5 and next1 < next9):
%o A374504             an, next1 = next1, next(g1)
%o A374504         else:
%o A374504             an, next9 = next9, next(g9)
%o A374504 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Jul 13 2024
%Y A374504 Cf. A098795, A102663.
%K A374504 base,nonn
%O A374504 1,2
%A A374504 _Eric Angelini_, Jul 09 2024