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A029958 Numbers that are palindromic in base 13. 7
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)