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Link to original content: http://oeis.org/A319477
A319477 - OEIS
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A319477
Nonnegative integers which cannot be obtained by adding exactly two nonzero decimal palindromes.
5
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
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
KEYWORD
nonn,base
AUTHOR
Alois P. Heinz, Sep 19 2018
STATUS
approved