

A331556


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


2



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
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OFFSET

1,1


COMMENTS

When normalized over (0,1) by their respective palindromefree interval about a 196iterate, 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 196iterates referred to here come from the reverseandadd process generating A006960.


LINKS



FORMULA



EXAMPLE

The first term is 5 since 196191 = 5
The second term is 9 since 887878 = 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 Bruteforce
n = 196
while n < 10**15:
m = n
while m != int(str(m)[::1]): m+=1
print(nm, end=', ')
n = n + int(str(n)[::1])


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



