A331556 The lower (or left) offset of a 196-iterate (A006960) from the largest palindrome less than the iterate.

5, 9, 14, 99, 52, 89, 100, 407, 268, 10769, 10890, 99, 99, 4400, 8900, 9890, 10000, 97625, 1089, 3584, 99, 629882, 1099890, 10989, 926, 890000, 8491505, 10890099, 8229644, 9999989, 69923062, 10890000, 99099000, 43337905, 99990089, 962943454, 109890, 454649691

Offset: 1

Author

James D. Klein, Jan 20 2020

Keywords

• nonn
• base

Comments

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.

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

Examples

			The first term is 5 since 196-191 = 5
The second term is 9 since 887-878 = 9, etc.
		

Crossrefs

Cf. A006960, A331557, A331560.

Programs

Mathematica

Map[Block[{k = # - 1}, While[k != IntegerReverse@ k, k--]; # - k] &, NestList[# + IntegerReverse[#] &, 196, 25]] (* brute force, or *)
Map[# - Block[{n = #, w, len, ww}, w = IntegerDigits[n]; len = Length@ w; ww = Take[w, Ceiling[len/2] ]; If[# < n, #, FromDigits@ Flatten@{#, If[OddQ@ len, Reverse@ Most@ #, Reverse@ #]} &@ If[Last@ ww == 0, MapAt[# - 1 &, Most@ ww, -1]~Join~{9}, MapAt[# - 1 &, ww, -1]]] &@ FromDigits@ Flatten@ {ww, If[OddQ@ len, Reverse@ Most@ ww, Reverse@ ww]}] &, NestList[# + IntegerReverse[#] &, 196, 37]] (* Michael De Vlieger, Jan 22 2020 *)

Python

# Slow Brute-force
n = 196
while n < 10**15:
  m = n
  while m != int(str(m)[::-1]): m+=-1
  print(n-m, end=', ')
  n = n + int(str(n)[::-1])

Formula

a(n) = A331560(n) - A331557(n).

Extensions

More terms from Michael De Vlieger, Jan 22 2020