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%I #10 Jan 19 2020 05:01:22
%S 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,
%T 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,
%U 14,6,7,8,9,10,11,66,13,14,15,7,8,9,10,11,12,13
%N 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.
%C Leading zeros are forbidden in the decimal representation of n; however we allow leading zeros in the palindromic parts.
%H Rémy Sigrist, <a href="/A331472/b331472.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A331472/a331472.gp.txt">PARI program for A331472</a>
%F a(n) <= n with equality iff n belongs to A002113.
%e For n = 1664:
%e - we can split this number into "1" and "6" and "6" and "4",
%e - or into "1" and "66" and "4",
%e - hence a(1664) = max(16, 71) = 71.
%t 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 *)
%o (PARI) See Links section.
%Y Cf. A002113, A331471 (binary analog).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Jan 17 2020
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