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A362064 Lexicographically earliest sequence of distinct positive integers such that the digit "1" is neither present in a(n) nor in a(n) + a(n+1).

%I A362064 #21 Apr 07 2023 19:58:54
%S A362064 2,3,4,5,20,6,22,7,23,9,24,8,25,27,26,28,29,30,32,33,34,35,37,36,38,
%T A362064 39,40,42,43,44,45,47,46,48,49,50,200,52,202,53,203,54,204,55,205,57,
%U A362064 206,56,207,58,208,59,209,60,220,62,222,63,223,64,224,65,225,67
%N A362064 Lexicographically earliest sequence of distinct positive integers such that the digit "1" is neither present in a(n) nor in a(n) + a(n+1).
%H A362064 Michael S. Branicky, <a href="/A362064/b362064.txt">Table of n, a(n) for n = 1..10000</a>
%e A362064 2 + 3 = 5; 3 + 4 = 7; 4 + 5 = 9; but as 5 + 6 = 11 we cannot use 6 nor 7 (sum 12), 8 (sum 13) and 9 (sum 14); we cannot use the integers 10 to 19 (as a 1 is present in them), so a(5) = 20 as 5 + 20 = 25, etc.
%o A362064 (Python)
%o A362064 from itertools import islice
%o A362064 def jump1(n):
%o A362064     s = str(n)
%o A362064     return n if "1" not in s else int(s[:(i:=s.index("1"))]+"2"+"0"*(len(s)-i-1))
%o A362064 def agen(): # generator of terms
%o A362064     an, aset, mink = 2, {2}, 3
%o A362064     while True:
%o A362064         yield an
%o A362064         k = mink
%o A362064         while k in aset or "1" in str(an+k): k = jump1(k+1)
%o A362064         an = k
%o A362064         aset.add(an)
%o A362064         while mink in aset: mink = jump1(mink+1)
%o A362064 print(list(islice(agen(), 64))) # _Michael S. Branicky_, Apr 07 2023
%Y A362064 Cf. A052383, A299957.
%K A362064 base,nonn
%O A362064 1,1
%A A362064 _Eric Angelini_ and Cécile Angelini, Apr 07 2023
%E A362064 a(27) and beyond from _Michael S. Branicky_, Apr 07 2023