A029958 Numbers that are palindromic in base 13.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 170, 183, 196, 209, 222, 235, 248, 261, 274, 287, 300, 313, 326, 340, 353, 366, 379, 392, 405, 418, 431, 444, 457, 470, 483, 496, 510, 523, 536, 549, 562

Offset

1,3

Comments

Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 04 2020

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Javier Cilleruelo, Florian Luca and Lewis Baxter, Every positive integer is a sum of three palindromes, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, arXiv preprint, arXiv:1602.06208 [math.NT], 2017.

Patrick De Geest, Palindromic numbers beyond base 10.

Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.

Index entries for sequences that are an additive basis, order 3.

Formula

Sum_{n>=2} 1/a(n) = 3.55686013... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020

Mathematica

f[n_, b_]:=Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 13], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
Select[Range[0, 600], IntegerDigits[#, 13]==Reverse[IntegerDigits[#, 13]]&] (* Harvey P. Dale, Nov 16 2022 *)

Prog

(PARI) isok(n) = my(d=digits(n, 13)); d == Vecrev(d); \\ Michel Marcus, May 13 2017

Crossrefs

Palindromes in bases 2 through 12: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113, A029956, A029957.

Sequence in context: A048310 A043716 A296750 * A297280 A048324 A048337

Adjacent sequences: A029955 A029956 A029957 * A029959 A029960 A029961

Keyword

nonn,base,easy

Author

Patrick De Geest

Status

approved