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A331557 The upper (or right) offset of a 196-iterate (A006960) from the smallest palindrome greater than the iterate. 2

%I #27 Mar 18 2023 16:28:26

%S 6,1,96,11,48,11,10,693,732,231,110,10901,10901,5600,1100,110,1000,

%T 12375,108911,96416,99901,470118,110,1089011,999074,110000,2508495,

%U 109901,1770356,11,40076938,99110000,10901000,56662095,9911,137056546,1099890110,545350309

%N The upper (or right) offset of a 196-iterate (A006960) from the smallest palindrome greater than the iterate.

%C When normalized over (0,1) by their respective palindrome-free interval about a 196-iterate, it has been empirically observed that the frequency distribution of this sequence appears to be quite symmetric about 0.5, as well as fractal when plotting the distribution over decreasing bin sizes.

%C The 196-iterates referred to here come from the reverse-and-add process generating A006960.

%F a(n) = A331560(n) - A331556(n).

%e The first term is 6 since 202-196 = 6;

%e The second term is 1 since 888-887 = 1; etc.

%o (Python)

%o # Upper 196 offsets. Slow brute force

%o n = 196

%o while n < 10**15:

%o m = n

%o while m != int(str(m)[::-1]): m+=1

%o print(m-n)

%o n = n + int(str(n)[::-1])

%Y Cf. A006960, A331556, A006960.

%K nonn,base

%O 1,1

%A _James D. Klein_, Jan 20 2020

%E More terms from _Jinyuan Wang_, Feb 29 2020

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Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)