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 A029960 Numbers that are palindromic in base 15. 6
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 226, 241, 256, 271, 286, 301, 316, 331, 346, 361, 376, 391, 406, 421, 436, 452, 467, 482, 497, 512, 527, 542, 557, 572, 587, 602, 617 (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) = 3.66254285... (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, 15], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *) Select[Range@ 620, PalindromeQ@ IntegerDigits[#, 15] &] (* Michael De Vlieger, May 13 2017, Version 10.3 *) PROG (PARI) isok(n) = my(d=digits(n, 15)); d == Vecrev(d); \\ Michel Marcus, May 14 2017 (Python) from sympy import integer_log from gmpy2 import digits def A029960(n): if n == 1: return 0 y = 15*(x:=15**integer_log(n>>1, 15)[0]) return int((c:=n-x)*x+int(digits(c, 15)[-2::-1]or'0', 15) if n

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Last modified September 10 21:37 EDT 2024. Contains 375795 sequences. (Running on oeis4.)