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

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, 22, 11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 33, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 44, 22, 33, 33, 33, 33, 33, 33, 33, 33, 33, 55, 22, 33, 33, 33, 33, 33

Offset: 0

Author

N. J. A. Sloane, Sep 11 2015

Keywords

• nonn
• base

Comments

Every number is the sum of three palindromes.

Examples

			Initial values of n,p,q,r are:
0 0 0 0
1 1 0 0
2 1 1 0
3 1 1 1
4 2 1 1
5 2 2 1
6 2 2 2
7 3 3 1
...
25 9 9 7
26 9 9 8
27 9 9 9
28 11 11 6
29 11 11 7
30 11 11 8
...
33 11 11 11
34 22 11 1
...
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 0..10000
• Javier Cilleruelo, Florian Luca and Lewis Baxter, Every positive integer is a sum of three palindromes, arXiv: 1602.06208 [math.NT], 2017, Math. Comp. 87 (2018), 3023-3055.
• David Consiglio, Jr., Python program
• James Grime and Brady Haran, Every Number is the Sum of Three Palindromes, Numberphile video (2018)

Crossrefs

Cf. A002113, A261422, A261132.

If "smallest" is changed to "largest" we get a sequence which agrees with the palindromic floor function A261423 for at least 300 terms.

Extensions

Edited by Alois P. Heinz, Dec 29 2018