A341034 a(n) is the smallest positive integer such that n+a(n) contains the string n-a(n) as a substring. If no such number exists then a(n) = -1.

-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, 20, 20, 20, 25, 25, 25, 25, 25, 29, 30, 30, 30, 30, 33, 34, 35, 35, 35, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50

Offset: 1

Author

Scott R. Shannon, Feb 03 2021

Keywords

• sign
• base

Comments

Based on a search limit of 5*10^9 up to n = 200000 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.

The sequence contains long runs of consecutive terms with the same value, resulting in the image for the values having a staircase-like pattern. In the first 200000 terms the longest run is 88890 terms, starting from a(61110), all of which have a(n) = 50000.

Examples

			a(5) = 5 as 5+5 = 10 which contains 5-5 = 0 as a substring.
a(6) = 5 as 6+5 = 11 which contains 6-5 = 1 as a substring.
a(15) = 10 as 15+10 = 25 which contains 15-10 = 5 as a substring.
a(35) = 29 as 35+29 = 64 which contains 35-29 = 6 as a substring.
		

Links

• Scott R. Shannon, Line graph of the terms for n=5..6111.

Crossrefs

Cf. A341028 (reverse), A341035 (forward and reverse), A339403, A339144, A328095, A333410, A332703.