A331472 Consider the different ways to split the decimal representation of n into palindromic parts; a(n) is the greatest possible sum of the parts of such a split.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 22, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 33, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 44, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 55, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 66, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13
Offset: 0
Examples
For n = 1664: - we can split this number into "1" and "6" and "6" and "4", - or into "1" and "66" and "4", - hence a(1664) = max(17, 71) = 71.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
- Rémy Sigrist, PARI program for A331472
Programs
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Mathematica
palQ[w_] := w == Reverse@w; ric[tg_, cr_] := Block[{m = Length@tg, t}, If[m == 0, Sow@ Total[ FromDigits /@ cr], Do[ If[ palQ[t = Take[tg, k]], ric[Drop[tg, k], Join[ cr, {t}]]], {k, m}]]]; a[n_] := Max[ Reap[ ric[ IntegerDigits[n], {}]][[2, 1]]]; a /@ Range[0, 99] (* Giovanni Resta, Jan 19 2020 *) -
PARI
\\ See Links section.
Formula
a(n) <= n with equality iff n belongs to A002113.
Comments