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 A029953 Palindromic in base 6. 28
 0, 1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 37, 43, 49, 55, 61, 67, 74, 80, 86, 92, 98, 104, 111, 117, 123, 129, 135, 141, 148, 154, 160, 166, 172, 178, 185, 191, 197, 203, 209, 215, 217, 259, 301, 343, 385, 427, 434, 476, 518, 560, 602, 644, 651, 693, 735, 777, 819 (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 03 2020 LINKS T. D. Noe, 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) = 3.03303318... (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, 6], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *) PROG (Magma) [n: n in [0..900] | Intseq(n, 6) eq Reverse(Intseq(n, 6))]; // Vincenzo Librandi, Sep 09 2015 (PARI) ispal(n, b=6)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020 (Python) from gmpy2 import digits from sympy import integer_log def A029953(n): if n == 1: return 0 y = 6*(x:=6**integer_log(n>>1, 6)[0]) return int((c:=n-x)*x+int(digits(c, 6)[-2::-1]or'0', 6) if n

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Last modified September 14 13:32 EDT 2024. Contains 375921 sequences. (Running on oeis4.)