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A261916 Smallest p such that n can be written as n = p+q+r where p>=q>=r>=0 are palindromes.

%I A261916 #32 Jan 08 2025 11:00:07
%S A261916 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 A261916 22,11,22,22,22,22,22,22,22,22,22,33,22,22,22,22,22,22,22,22,22,22,44,
%U A261916 22,33,33,33,33,33,33,33,33,33,55,22,33,33,33,33,33
%N A261916 Smallest p such that n can be written as n = p+q+r where p>=q>=r>=0 are palindromes.
%C A261916 Every number is the sum of three palindromes.
%H A261916 David Consiglio, Jr., <a href="/A261916/b261916.txt">Table of n, a(n) for n = 0..10000</a>
%H A261916 Javier Cilleruelo, Florian Luca and Lewis Baxter, <a href="https://arxiv.org/abs/1602.06208">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.</a> 87 (2018), 3023-3055.
%H A261916 David Consiglio, Jr., <a href="/A261916/a261916_1.txt">Python program</a>
%H A261916 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 A261916 Initial values of n,p,q,r are:
%e A261916 0 0 0 0
%e A261916 1 1 0 0
%e A261916 2 1 1 0
%e A261916 3 1 1 1
%e A261916 4 2 1 1
%e A261916 5 2 2 1
%e A261916 6 2 2 2
%e A261916 7 3 3 1
%e A261916 ...
%e A261916 25 9 9 7
%e A261916 26 9 9 8
%e A261916 27 9 9 9
%e A261916 28 11 11 6
%e A261916 29 11 11 7
%e A261916 30 11 11 8
%e A261916 ...
%e A261916 33 11 11 11
%e A261916 34 22 11 1
%e A261916 ...
%Y A261916 Cf. A002113, A261422, A261132.
%Y A261916 If "smallest" is changed to "largest" we get a sequence which agrees with the palindromic floor function A261423 for at least 300 terms.
%K A261916 nonn,base
%O A261916 0,5
%A A261916 _N. J. A. Sloane_, Sep 11 2015
%E A261916 Edited by _Alois P. Heinz_, Dec 29 2018