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

1,1

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.

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

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

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 *)

Prog

(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])

Crossrefs

Cf. A006960, A331557, A331560.

Sequence in context: A115380 A107980 A163161 * A188358 A228218 A361993

Adjacent sequences: A331553 A331554 A331555 * A331557 A331558 A331559

Keyword

nonn,base

Author

James D. Klein, Jan 20 2020

Extensions

More terms from Michael De Vlieger, Jan 22 2020

Status

approved