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A029955 Palindromic in base 9. 32
0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 82, 91, 100, 109, 118, 127, 136, 145, 154, 164, 173, 182, 191, 200, 209, 218, 227, 236, 246, 255, 264, 273, 282, 291, 300, 309, 318, 328, 337, 346, 355, 364, 373, 382, 391, 400, 410, 419, 428, 437 (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
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.
Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.
FORMULA
Sum_{n>=2} 1/a(n) = 3.29797695... (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, 9], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
PROG
(Python)
from gmpy2 import digits
def palQgen(l, b): # generator of palindromes in base b of length <= 2*l
if l > 0:
yield 0
for x in range(1, l+1):
for y in range(b**(x-1), b**x):
s = digits(y, b)
yield int(s+s[-2::-1], b)
for y in range(b**(x-1), b**x):
s = digits(y, b)
yield int(s+s[::-1], b)
A029955_list = list(palQgen(4, 9)) # Chai Wah Wu, Dec 01 2014
(Python)
from gmpy2 import digits
def A029955(n):
if n == 1: return 0
y = 9*(x:=9**(len(digits(n>>1, 9))-1))
return int((c:=n-x)*x+int(digits(c, 9)[-2::-1]or'0', 9) if n<x+y else (c:=n-y)*y+int(digits(c, 9)[-1::-1]or'0', 9)) # Chai Wah Wu, Jun 14 2024
(PARI) ispal(n, b=9)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020
CROSSREFS
Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113.
Sequence in context: A048306 A043712 A296709 * A297268 A048320 A037407
KEYWORD
nonn,base,easy,changed
AUTHOR
STATUS
approved

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Last modified June 25 18:39 EDT 2024. Contains 373707 sequences. (Running on oeis4.)