A261675 Minimal number of palindromes in base 10 that add to n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2

Offset: 0

Author

N. J. A. Sloane, Sep 02 2015

Keywords

• nonn
• base

Comments

This sequence coincides with A088601 for n <= 301, but differs at n=302.

Although A088601 and this sequence agree for a large number of terms, because of their importance they warrant separate entries.

Cilleruelo and Luca prove that a(n) <= 3 (in fact they prove this for any fixed base g>=5). - Danny Rorabaugh, Feb 26 2016

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000
• Javier Cilleruelo and Florian Luca, Every positive integer is a sum of three palindromes, arXiv preprint arXiv:1602.06208 [math.NT], 2016.
• William D. Banks, Every natural number is the sum of forty-nine palindromes, INTEGERS 17 (2016), 9 pp.
• James Grime and Brady Haran, Every Number is the Sum of Three Palindromes (2018), Numberphile video

Crossrefs

Cf. A002113, A035137, A088601, A260255, A261422.

Programs

PARI

ispal(n)=my(d=digits(n)); d==Vecrev(d);
a(n)=my(L=n\2,d,e); if(ispal(n), return(1)); d=[1]; while((e=fromdigits(d))<=L, if(ispal(n-e), return(2)); my(k=#d,i=(k+1)\2); while(i&&d[i]==9, d[i]=0; d[k+1-i]=0; i--); if(i, d[i]++; d[k+1-i]=d[i], d=vector(#d+1); d[1]=d[#d]=1)); 3; \\ Charles R Greathouse IV, Nov 12 2018