A341028 a(n) is the smallest positive integer such that n+a(n) contains the string n-a(n) in reverse 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, 9, 15, 15, 20, 20, 20, 20, 20, 25, 25, 25, 9, 25, 29, 30, 30, 30, 30, 33, 34, 35, 35, 9, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 9, 50, 50, 50, 50, 55, 41, 51, 52, 53, 54, 9, 60, 60, 60, 65, 50, 32, 52, 53, 54, 70, 9

Offset

1,5

Comments

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 a(n) = -1.

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.

Numerous patterns exist in the values of a(n), e.g., when a(n) consists of all 9's and n is not a power of 10 then n is palindromic.

Links

Table of n, a(n) for n=1..77.

Scott R. Shannon, Image of the terms for n = 5..300000. It is possible the frame-like pattern continues to larger and larger scales resulting in a fractal structure.

Example

a(5) = 5 as 5+5 = 10 which contains reverse(5-5) = reverse(0) = 0 as a substring.
a(6) = 5 as 6+5 = 11 which contains reverse(6-5) = reverse(1) = 1 as a substring.
a(15) = 10 as 15+10 = 25 which contains reverse(15-10) = reverse(5) = 5 as a substring.
a(22) = 9 as 22+9 = 31 which contains reverse(22-9) = reverse(13) = 31 as a substring.

Crossrefs

Cf. A341034 (forward), A341035 (forward and reverse), A339403, A339144, A328095, A333410, A332703.

Sequence in context: A021022 A010716 A032560 * A341034 A341035 A200325

Adjacent sequences: A341025 A341026 A341027 * A341029 A341030 A341031

Keyword

sign,look,base

Author

Scott R. Shannon, Feb 02 2021

Status

approved