A253241 - OEIS

%I #17 Apr 19 2015 20:38:51

%S 0,2,4,6,8,10,13,39,65,91,117,143,13,26,39,52,65,78,91,104,117,130,

%T 143,169,26,39,52,65,78,91,104,117,130,143,169,169,39,52,65,78,91,104,

%U 117,130,143,169,169,507,52,65,78,91,104,117,130,143,169,169,507,676,65,78,91,104,117

%N 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.)

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

%C a(237) is conjectured to be -1.

%C A060382 lists the smallest possible Lychrel number in base n.

%e a(29) = 91 since (in duodecimal) 25 (decimal 29) + 52 = 77 (decimal 91) and 77 is a palindrome.

%e a(69) = 507 since (in duodecimal) 59 (decimal 69) + 95 = 132, 132 + 231 = 363 (decimal 507) and 363 is a palindrome.

%e a(105) = 1885 since (in duodecimal) 89 (decimal 105) + 98 = 165, 165 + 561 = 706, 706 + 607 = 1111 (decimal 1885) and 1111 is a palindrome.

%t 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}]

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

%K nonn,base,easy

%O 0,2

%A _Eric Chen_, Apr 07 2015