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

1,1

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.)

Links

Table of n, a(n) for n=1..34.

Formula

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

Example

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

Prog

(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])

Crossrefs

Cf. A006960, A331556, A331557.

Sequence in context: A304747 A304749 A105028 * A014550 A367547 A070836

Adjacent sequences: A331557 A331558 A331559 * A331561 A331562 A331563

Keyword

nonn,base

Author

James D. Klein, Jan 20 2020

Extensions

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

Status

approved