A319477 Nonnegative integers which cannot be obtained by adding exactly two nonzero decimal palindromes.

0, 1, 21, 32, 43, 54, 65, 76, 87, 98, 111, 131, 141, 151, 161, 171, 181, 191, 201, 1031, 1041, 1042, 1051, 1052, 1053, 1061, 1062, 1063, 1064, 1071, 1072, 1073, 1074, 1075, 1081, 1082, 1083, 1084, 1085, 1086, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1099

Offset

1,3

Comments

Every integer larger than two can be obtained by adding exactly three nonzero decimal palindromes.

The nonzero palindromes of this sequence are in A213879.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..65536

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.

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

Formula

A319468(a(n)) = 0.

Maple

p:= proc(n) option remember; local i, s; s:= ""||n;
      for i to iquo(length(s), 2) do if
        s[i]<>s[-i] then return false fi od; true
    end:
h:= proc(n) option remember; `if`(n<1, 0,
     `if`(p(n), n, h(n-1)))
    end:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
      0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
    end:
g:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(2):
a:= proc(n) option remember; local j; for j from 1+
      `if`(n=1, -1, a(n-1)) while g(j)<>0 do od; j
    end:
seq(a(n), n=1..80);

Crossrefs

Cf. A002113, A035137 (allowing zero), A213879, A261131, A319453, A319468, A319586.

Sequence in context: A168005 A118535 A127423 * A035137 A261910 A351842

Adjacent sequences: A319474 A319475 A319476 * A319478 A319479 A319480

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved