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.
FORMULA
Sum_{n>=2} 1/a(n) = 3.6112482... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
EXAMPLE
195 is DD in base 14.
196 is 100 in base 14, so it's not in the sequence.
197 is 101 in base 14.
MATHEMATICA
palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[ Range[0, 600], palQ[#, 14] &] (* Harvey P. Dale, Aug 03 2014 *)
PROG
(PARI) isok(n) = Pol(d=digits(n, 14)) == Polrev(d); \\ Michel Marcus, Mar 12 2017
(Python)
from sympy import integer_log
from gmpy2 import digits
def A029959(n):
if n == 1: return 0
y = 14*(x:=14**integer_log(n>>1, 14)[0])
return int((c:=n-x)*x+int(digits(c, 14)[-2::-1]or'0', 14) if n<x+y else (c:=n-y)*y+int(digits(c, 14)[-1::-1]or'0', 14)) # Chai Wah Wu, Jun 14 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved