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

0,3

Comments

Leading zeros are forbidden in the decimal representation of n; however we allow leading zeros in the palindromic parts.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program for A331472

Formula

a(n) <= n with equality iff n belongs to A002113.

Example

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(16, 71) = 71.

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 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A002113, A331471 (binary analog).

Sequence in context: A084051 A069652 A055483 * A364362 A059717 A004185

Adjacent sequences: A331469 A331470 A331471 * A331473 A331474 A331475

Keyword

nonn,base

Author

Rémy Sigrist, Jan 17 2020

Status

approved