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%I #30 Dec 29 2018 20:19:14
%S 0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,11,11,11,11,
%T 22,11,22,22,22,22,22,22,22,22,22,33,22,22,22,22,22,22,22,22,22,22,44,
%U 22,33,33,33,33,33,33,33,33,33,55,22,33,33,33,33,33
%N Smallest p such that n can be written as n = p+q+r where p>=q>=r>=0 are palindromes.
%C Every number is the sum of three palindromes.
%H David Consiglio, Jr., <a href="/A261916/b261916.txt">Table of n, a(n) for n = 0..10000</a>
%H Javier Cilleruelo, Florian Luca and Lewis Baxter, <a href="http://arxiv.org/abs/1602.06208v2">Every positive integer is a sum of three palindromes</a>, arXiv: 1602.06208 [math.NT], 2017, <a href="https://doi.org/10.1090/mcom/3221">Math. Comp., published electronically: August 15, 2017.
%H David Consiglio, Jr., <a href="/A261916/a261916_1.txt">Python program</a>
%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=OKhacWQ2fCs">Every Number is the Sum of Three Palindromes</a>, Numberphile video (2018)
%e Initial values of n,p,q,r are:
%e 0 0 0 0
%e 1 1 0 0
%e 2 1 1 0
%e 3 1 1 1
%e 4 2 1 1
%e 5 2 2 1
%e 6 2 2 2
%e 7 3 3 1
%e ...
%e 25 9 9 7
%e 26 9 9 8
%e 27 9 9 9
%e 28 11 11 6
%e 29 11 11 7
%e 30 11 11 8
%e ...
%e 33 11 11 11
%e 34 22 11 1
%e ...
%Y Cf. A002113, A261422, A261132.
%Y If "smallest" is changed to "largest" we get a sequence which agrees with the palindromic floor function A261423 for at least 300 terms.
%K nonn,base
%O 0,5
%A _N. J. A. Sloane_, Sep 11 2015
%E Edited by _Alois P. Heinz_, Dec 29 2018
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