A331560 Size of the palindrome-free intervals about the 196-iterates, A006960.

11, 10, 110, 110, 100, 100, 110, 1100, 1000, 11000, 11000, 11000, 11000, 10000, 10000, 10000, 11000, 110000, 110000, 100000, 100000, 1100000, 1100000, 1100000, 1000000, 1000000, 11000000, 11000000, 10000000, 10000000, 110000000, 110000000, 110000000, 100000000

Offset: 1

Author

James D. Klein, Jan 20 2020

Keywords

• nonn
• base

Comments

By empirical observation, the integers in this sequence are of the form 10*10^n and 11*10^n, n >= 0, since they are the difference of consecutive palindromes surrounding the 196-iterates. (No differences of 2 observed.)

Examples

			191 < 196 < 202, 202 - 191 = 11;
878 < 887 < 888, 888 - 878 = 10; etc.
		

Crossrefs

Cf. A006960, A331556, A331557.

Programs

Python

# Palindrome-free interval about 196 offsets. Slow brute-force
n = 196
while n < 10**15:
     m = n
     while m != int(str(m)[::-1]): m+=1
     s = m
     m = n
     while m != int(str(m)[::-1]): m-=1
     print(s-m)
     n = n + int(str(n)[::-1])

Formula

a(n) = A331556(n) + A331557(n).

Extensions

a(31)-a(34) from Jinyuan Wang, Feb 29 2020