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A029954
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Palindromic in base 7.
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30
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0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 50, 57, 64, 71, 78, 85, 92, 100, 107, 114, 121, 128, 135, 142, 150, 157, 164, 171, 178, 185, 192, 200, 207, 214, 221, 228, 235, 242, 250, 257, 264, 271, 278, 285, 292, 300, 307, 314, 321, 328, 335, 342, 344, 400, 456
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refs;
listen;
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internal format)
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OFFSET
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1,3
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COMMENTS
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Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 03 2020
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LINKS
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FORMULA
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Sum_{n>=2} 1/a(n) = 3.1313768... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
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MATHEMATICA
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f[n_, b_] := Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 7], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
pal7Q[n_]:=Module[{idn7=IntegerDigits[n, 7]}, idn7==Reverse[idn7]]; Select[ Range[0, 500], pal7Q] (* Harvey P. Dale, Jul 30 2015 *)
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PROG
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(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)
(Python)
from gmpy2 import digits
from sympy import integer_log
if n == 1: return 0
y = 7*(x:=7**integer_log(n>>1, 7)[0])
return int((c:=n-x)*x+int(digits(c, 7)[-2::-1]or'0', 7) if n<x+y else (c:=n-y)*y+int(digits(c, 7)[-1::-1]or'0', 7)) # Chai Wah Wu, Jun 14 2024
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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