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A261675 Minimal number of palindromes in base 10 that add to n. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

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

PROG

(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

CROSSREFS

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

Sequence in context: A163376 A261913 A088601 * A028950 A094916 A036485

Adjacent sequences:  A261672 A261673 A261674 * A261676 A261677 A261678

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Sep 02 2015

STATUS

approved

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Last modified March 19 17:21 EDT 2019. Contains 321330 sequences. (Running on oeis4.)