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 A331556 The lower (or left) offset of a 196-iterate (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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)