A331560 -id:A331560 - cp's OEIS frontend

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

James D. Klein, Jan 20 2020

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.

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

Cf. A006960, A331557, A331560.

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 *)

# 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])

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

More terms from Michael De Vlieger, Jan 22 2020

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

Original entry on oeis.org

6, 1, 96, 11, 48, 11, 10, 693, 732, 231, 110, 10901, 10901, 5600, 1100, 110, 1000, 12375, 108911, 96416, 99901, 470118, 110, 1089011, 999074, 110000, 2508495, 109901, 1770356, 11, 40076938, 99110000, 10901000, 56662095, 9911, 137056546, 1099890110, 545350309

Offset: 1

James D. Klein, Jan 20 2020

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

			The first term is 6 since 202-196 = 6;
The second term is 1 since 888-887 = 1; etc.

Cf. A006960, A331556, A006960.

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

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

More terms from Jinyuan Wang, Feb 29 2020

cp's OEIS Frontend

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

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