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A305409
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Positive numbers that can be expressed as the product of 1 or more binary palindromes (elements of A006995).
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1
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1, 3, 5, 7, 9, 15, 17, 21, 25, 27, 31, 33, 35, 45, 49, 51, 63, 65, 73, 75, 81, 85, 93, 99, 105, 107, 119, 125, 127, 129, 135, 147, 153, 155, 165, 175, 189, 195, 217, 219, 225, 231, 243, 245, 255, 257, 273, 279, 289, 297, 313, 315, 321, 325, 341, 343, 357, 365
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OFFSET
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1,2
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LINKS
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EXAMPLE
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155 is in the sequence because it is 5*31, and both 5 and 31 are palindromic numbers (with binary representations 101 and 11111, respectively).
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MAPLE
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dmax:= 10: N:= 2^dmax: # to get all terms < N
revdigs:= proc(n)
local L, Ln, i;
L:= convert(n, base, 2);
Ln:= nops(L);
add(L[i]*2^(Ln-i), i=1..Ln);
end proc:
A:= {}:
for d from 2 to dmax do
if d::even then
A:= A union {seq(2^(d/2)*x + revdigs(x), x=2^(d/2-1)..2^(d/2)-1)}
else
m:= (d-1)/2;
B:={seq(2^(m+1)*x + revdigs(x), x=2^(m-1)..2^m-1)};
A:= A union B union map(`+`, B, 2^m)
fi
od:
R:= {1}:
for b in A do
R:= map(t -> seq(t*b^j, j=0..floor(log[b](N/t))), R)
od:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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