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A261675
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Minimal number of palindromes in base 10 that add to n.
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12
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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
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OFFSET
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0,11
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COMMENTS
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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
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LINKS
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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
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PROG
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(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
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CROSSREFS
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Cf. A002113, A035137, A088601, A260255, A261422.
Sequence in context: A163376 A261913 A088601 * A028950 A094916 A036485
Adjacent sequences: A261672 A261673 A261674 * A261676 A261677 A261678
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Sep 02 2015
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STATUS
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approved
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