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Smallest p such that n can be written as n = p+q+r where p>=q>=r>=0 are palindromes.
1

%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