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.

-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, 50, 50, 50, 50, 50, 55, 50, 51, 52, 53, 54, 60, 60, 60, 60, 65, 50, 50, 65, 65, 70, 70, 70

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 no a(n) exists.

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.

Links

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

Scott R. Shannon, Image of the terms for n=5..100000.

Example

a(5) = 5 as 5+5 = 10 which contains both 5-5 = 0 and reverse(0) = 0 as a substring.
a(15) = 10 as 15+10 = 25 which contains both 15-10 = 5 and reverse(5) = 5 as a substring.
a(61) = 50 as 61+50 = 111 which contains both 51-50 = 11 and reverse(11) = 11 as a substring.
a(71) = 50 as 71+50 = 121 which contains both 71-50 = 21 and reverse(21) = 12 as a substring.
a(1902) = 1829 as 1902+1829 = 3731 which contains both 1902-1829 = 73 and reverse(73) = 37 as a substring.

Crossrefs

Cf. A341034 (forward), A341028 (reverse), A339403, A339144, A328095, A333410, A332703.

Sequence in context: A032560 A341028 A341034 * A200325 A372613 A355588

Adjacent sequences: A341032 A341033 A341034 * A341036 A341037 A341038

Keyword

sign,base

Author

Scott R. Shannon, Feb 03 2021

Status

approved