A241174 Smallest number requiring n steps to reach a palindrome under the "add a digit" process described in A241173.

0, 10, 13, 12, 17, 89, 1072, 1066, 1058, 1049, 1045, 1039, 1036, 1028, 1019, 1017, 1009, 1007, 998, 994, 988, 100953, 100944, 100935, 100926, 100917, 100908, 100899, 100890, 100882, 100874, 100866, 100858, 100849, 100841, 100833, 100825, 100817, 100809, 100801, 100792, 100784, 100777

Offset: 0

Author

N. J. A. Sloane, Apr 23 2014

Keywords

• nonn
• base

Comments

Beginning with a(6), the palindromic sinks appear to be, for positive n, (10^n+1)*(10^(n+1)+1):

n=1 a(6)-a(20) 1072 to 988

n=2 a(21)-a(157) 100953 to 99980

n=3 a(158)-a(1461) 10^7+9827 to 10^7-20

n=4 a(1462)-a(14078) 10^9+98720 to 10^9-20

n=5 a(14079)-a(137233) 10^11+988091 to 10^11-20

n=6 a(137234)-a(1346435) 10^13+9885167 to 10^13-20

n=7 a(1346436)-a(13265907) 10^15+98879696 to 10^15-20

etc. - Hans Havermann, Apr 23 2014

References

• Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014

Links

• Hans Havermann, Table of n, a(n) for n = 0..1500

Crossrefs

Cf. A241173, A002113.

Related sequences: A241173, A241174, A241175, A241176, A241177, A241178, A241179, A241180, A241181, A241182, A241183.

Programs

Mathematica

A241173[n_] := Module[{c, nx},
   If[n == IntegerReverse[n], Return[0]];
   c = 1; nx = n;
   While[ ! AnyTrue[nx = Union[Flatten[nx + IntegerDigits[nx]]], # == IntegerReverse[#] &], c++];
   Return[c]];
A241174[n_] := Module[{i = 0},
   While[A241173[i] != n, i++];
   Return[i]];
Table[A241174[i], {i, 0, 5}] (* Robert Price, Mar 17 2019 *)

Extensions

More terms from Hans Havermann, Apr 23 2014