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A341035 a(n) is the smallest positive integer such that n+a(n) contains the string n-a(n), in both forward and reverse directions, as a substring. If no such number exists then a(n) = -1.

%I A341035 #15 Feb 05 2021 00:18:20
%S A341035 -1,-1,-1,-1,5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,15,15,15,15,15,20,20,
%T A341035 20,20,20,25,25,25,25,25,29,30,30,30,30,33,34,35,35,35,37,38,39,40,40,
%U A341035 41,42,43,44,45,50,50,50,50,50,55,50,51,52,53,54,60,60,60,60,65,50,50,65,65,70,70,70
%N A341035 a(n) is the smallest positive integer such that n+a(n) contains the string n-a(n), in both forward and reverse directions, as a substring. If no such number exists then a(n) = -1.
%C A341035 Based on a search limit of 5*10^9 up to n = 300000 the values of n for which no a(n) is found are n = 1,2,3,4. This is likely the complete list of values for which no a(n) exists.
%C A341035 The longest run of consecutive terms with the same value in the first 300000 terms is the run of 5's at the beginning of the sequence, ten in all. This is likely the longest run for all numbers.
%H A341035 Scott R. Shannon, <a href="/A341035/a341035.png">Image of the terms for n=5..100000</a>.
%e A341035 a(5) = 5 as 5+5 = 10 which contains both 5-5 = 0 and reverse(0) = 0 as a substring.
%e A341035 a(15) = 10 as 15+10 = 25 which contains both 15-10 = 5 and reverse(5) = 5 as a substring.
%e A341035 a(61) = 50 as 61+50 = 111 which contains both 51-50 = 11 and reverse(11) = 11 as a substring.
%e A341035 a(71) = 50 as 71+50 = 121 which contains both 71-50 = 21 and reverse(21) = 12 as a substring.
%e A341035 a(1902) = 1829 as 1902+1829 = 3731 which contains both 1902-1829 = 73 and reverse(73) = 37 as a substring.
%Y A341035 Cf. A341034 (forward), A341028 (reverse), A339403, A339144, A328095, A333410, A332703.
%K A341035 sign,base
%O A341035 1,5
%A A341035 _Scott R. Shannon_, Feb 03 2021