A250412 Palindromic in bases 10 and 36.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1221, 1441, 2882, 5115, 12321, 16861, 19491, 21112, 30803, 33433, 36063, 37973, 42224, 159951, 741147, 987789, 1301031, 1867681, 3315133, 4306034, 5182815, 5927295, 6918196, 6950596, 9242429, 9488849, 10066001, 48655684

Offset: 1

Author

Robert G. Wilson v, Nov 23 2014

Keywords

• nonn
• base

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..93

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165.

Programs

Magma

[n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 36) eq Reverse(Intseq(n, 36))]; // Vincenzo Librandi, Nov 23 2014

Mathematica

palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; genPal[n_] := Block[{id = IntegerDigits@ n, insert = {{}, {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}}, FromDigits@ Join[id, #, Reverse@ id] & /@ insert]; k = 1; lst = {0, 1, 2, 3,  4, 5, 6, 7, 8, 9}; While[k < 1000001, s = Select[ genPal[k], palQ[#, 36] &]; If[s != {}, AppendTo[lst, s]; Print@ s; lst = Sort@ Flatten@ lst]; k++]; lst
b1=10; b2=36; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Nov 23 2014 *)
Select[Range[0,49*10^6],PalindromeQ[#]&&IntegerDigits[#,36]== Reverse[ IntegerDigits[ #,36]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 04 2019 *)