cp's OEIS Frontend

A029957 Numbers that are palindromic in base 12.

%I A029957 #30 Jun 14 2024 11:59:19
%S A029957 0,1,2,3,4,5,6,7,8,9,10,11,13,26,39,52,65,78,91,104,117,130,143,145,
%T A029957 157,169,181,193,205,217,229,241,253,265,277,290,302,314,326,338,350,
%U A029957 362,374,386,398,410,422,435,447,459,471,483,495,507,519,531
%N A029957 Numbers that are palindromic in base 12.
%C A029957 Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - _Charles R Greathouse IV_, May 04 2020
%H A029957 John Cerkan, <a href="/A029957/b029957.txt">Table of n, a(n) for n = 1..10000</a>
%H A029957 Javier Cilleruelo, Florian Luca and Lewis Baxter, <a href="https://doi.org/10.1090/mcom/3221">Every positive integer is a sum of three palindromes</a>, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, <a href="http://arxiv.org/abs/1602.06208">arXiv preprint</a>, arXiv:1602.06208 [math.NT], 2017.
%H A029957 Patrick De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>.
%H A029957 Phakhinkon Phunphayap and Prapanpong Pongsriiam, <a href="https://doi.org/10.13140/RG.2.2.23202.79047">Estimates for the Reciprocal Sum of b-adic Palindromes</a>, 2019.
%H A029957 <a href="/index/Ab#basis_03">Index entries for sequences that are an additive basis</a>, order 3.
%F A029957 Sum_{n>=2} 1/a(n) = 3.4989489... (Phunphayap and Pongsriiam, 2019). - _Amiram Eldar_, Oct 17 2020
%t A029957 f[n_,b_]:=Module[{i=IntegerDigits[n,b]},i==Reverse[i]];lst={};Do[If[f[n,12],AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2009 *)
%o A029957 (PARI) isok(n) = my(d=digits(n, 12)); d == Vecrev(d); \\ _Michel Marcus_, May 13 2017
%o A029957 (Python)
%o A029957 from sympy import integer_log
%o A029957 from gmpy2 import digits
%o A029957 def A029957(n):
%o A029957     if n == 1: return 0
%o A029957     y = 12*(x:=12**integer_log(n>>1,12)[0])
%o A029957     return int((c:=n-x)*x+int(digits(c,12)[-2::-1]or'0',12) if n<x+y else (c:=n-y)*y+int(digits(c,12)[-1::-1]or'0',12)) # _Chai Wah Wu_, Jun 14 2024
%Y A029957 Cf. A029958, A029959, A029960 (in bases 13..15).
%K A029957 nonn,base,easy
%O A029957 1,3
%A A029957 _Patrick De Geest_