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A029956
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Numbers that are palindromic in base 11.
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9
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 122, 133, 144, 155, 166, 177, 188, 199, 210, 221, 232, 244, 255, 266, 277, 288, 299, 310, 321, 332, 343, 354, 366, 377, 388, 399, 410, 421, 432, 443, 454, 465, 476, 488, 499
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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 04 2020
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LINKS
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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.
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FORMULA
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Sum_{n>=2} 1/a(n) = 3.4369816... (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, 11], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
pal11Q[n_]:=Module[{idn11=IntegerDigits[n, 11]}, idn11==Reverse[idn11]]; Select[Range[0, 500], pal11Q] (* Harvey P. Dale, May 11 2015 *)
Select[Range[0, 500], PalindromeQ[IntegerDigits[#, 11]] &] (* Michael De Vlieger, May 12 2017, Version 10.3 *)
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PROG
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(PARI) ispal(n, b)=my(tmp, d=log(n+.5)\log(b)-1); while(d, tmp=n%b; n\=b; if(n\b^d!=tmp, return(0)); n=n%(b^d); d-=2; ); d<0||n%(b+1)==0
is(n)=ispal(n, 11) \\ Charles R Greathouse IV, Aug 21 2012
(PARI) ispal(n, b=11)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 04 2020
(Sage)
[n for n in (0..499) if Word(n.digits(11)).is_palindrome()] # Peter Luschny, Sep 13 2018
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CROSSREFS
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Cf. A002113 (base 10), A029957 (base 12).
Sequence in context: A048308 A043714 A296744 * A297274 A048322 A048335
Adjacent sequences: A029953 A029954 A029955 * A029957 A029958 A029959
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KEYWORD
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nonn,base,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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