A253241 The "Reverse and Add!" problem in base 12: sequence lists the final palindrome number for n, or -1 if no palindrome is ever reached. (Written in base 10.)

0, 2, 4, 6, 8, 10, 13, 39, 65, 91, 117, 143, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 169, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 169, 169, 39, 52, 65, 78, 91, 104, 117, 130, 143, 169, 169, 507, 52, 65, 78, 91, 104, 117, 130, 143, 169, 169, 507, 676, 65, 78, 91, 104, 117

Offset

0,2

Comments

Is a(n) = -1 possible? All numbers below 100 (decimal 144) reach a palindrome.

a(237) is conjectured to be -1.

A060382 lists the smallest possible Lychrel number in base n.

Links

Table of n, a(n) for n=0..64.

Example

a(29) = 91 since (in duodecimal) 25 (decimal 29) + 52 = 77 (decimal 91) and 77 is a palindrome.
a(69) = 507 since (in duodecimal) 59 (decimal 69) + 95 = 132, 132 + 231 = 363 (decimal 507) and 363 is a palindrome.
a(105) = 1885 since (in duodecimal) 89 (decimal 105) + 98 = 165, 165 + 561 = 706, 706 + 607 = 1111 (decimal 1885) and 1111 is a palindrome.

Mathematica

tol = 1728; r[n_] := FromDigits[Reverse[IntegerDigits[n, 12]], 12]; palQ[n_] := n == r[n]; ar[n_] := n + r[n]; Table[k = 0; If[palQ[n], n = ar[n]; k = 1]; While[! palQ[n] && k < tol, n = ar[n]; k++]; If[k == tol, n = -1]; n, {n, 0, 144}]

Crossrefs

Cf. A061563, A062129, A016016, A060382, A029957.

Sequence in context: A085577 A331130 A121832 * A337972 A302979 A006586

Adjacent sequences: A253238 A253239 A253240 * A253242 A253243 A253244

Keyword

nonn,base,easy

Author

Eric Chen, Apr 07 2015

Status

approved