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

0,5

Comments

Every number is the sum of three palindromes.

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., published electronically: August 15, 2017.

David Consiglio, Jr., Python program

James Grime and Brady Haran, Every Number is the Sum of Three Palindromes, Numberphile video (2018)

Example

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
...

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.

Sequence in context: A086161 A008620 A104581 * A113675 A020912 A194990

Adjacent sequences: A261913 A261914 A261915 * A261917 A261918 A261919

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 11 2015

Extensions

Edited by Alois P. Heinz, Dec 29 2018

Status

approved