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A029952
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Palindromic in base 5.
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29
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0, 1, 2, 3, 4, 6, 12, 18, 24, 26, 31, 36, 41, 46, 52, 57, 62, 67, 72, 78, 83, 88, 93, 98, 104, 109, 114, 119, 124, 126, 156, 186, 216, 246, 252, 282, 312, 342, 372, 378, 408, 438, 468, 498, 504, 534, 564, 594, 624, 626, 651, 676, 701, 726, 756, 781, 806, 831
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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) = 2.9200482... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
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MAPLE
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b:=5;
ispal := proc(n) global b; local t1, t2, i;
if n <= b-1 then return(1); fi;
t1:=convert(n, base, b); t2:=nops(t1);
for i from 1 to floor(t2/2) do
if t1[i] <> t1[t2+1-1] then return(-1); fi;
od: return(1); end;
lis:=[]; for n from 0 to 100 do if ispal(n) = 1 then lis:=[op(lis), n]; fi; od: lis;
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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, 5], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
Select[Range[0, 1000], IntegerDigits[#, 5]==Reverse[IntegerDigits[#, 5]]&] (* Harvey P. Dale, Oct 24 2020 *)
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PROG
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(Magma) [n: n in [0..900] | Intseq(n, 5) eq Reverse(Intseq(n, 5))]; // Vincenzo Librandi, Sep 09 2015
(Python)
from gmpy2 import digits
if n == 1: return 0
y = 5*(x:=5**(len(digits(n>>1, 5))-1))
return int((c:=n-x)*x+int(digits(c, 5)[-2::-1]or'0', 5) if n<x+y else (c:=n-y)*y+int(digits(c, 5)[-1::-1]or'0', 5)) # Chai Wah Wu, Jun 13 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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