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A241491
2*n is not the sum of two base-2 palindromes
7
88, 94, 104, 121, 122, 155, 262, 314, 328, 368, 377, 397, 416, 431, 433, 434, 440, 466, 472, 497, 500, 590, 620, 654, 655, 664, 671, 676, 688, 704, 710, 716, 720, 905, 945, 961, 973, 977, 1063, 1103, 1114, 1131, 1228, 1234, 1249, 1250, 1270, 1312, 1343, 1348
OFFSET
1,1
COMMENTS
Note that since all nonzero base-2 palindromes are odd, the sum of two nonzero base-2 palindromes is even.
LINKS
EXAMPLE
86 is not in the sequence because 2*86 = 7 + 165, and 7 and 165 are in A006995.
MAPLE
N:= 15; # for all entries up to 2^(N-1)
with(SignalProcessing): # requires Maple 17+
rev2:= proc(n) option remember;
rev2(floor(n/2)) + (n mod 2)*2^ilog2(n)
end;
rev2(0) := 0; rev2(1):= 1;
B:= Array(1..2^N, datatype=float[8]);
for d from 1 to N do
d1:= ceil(d/2);
for x from 2^(d1-1) to 2^d1-1 do
if d::even then y:= x*2^d1+rev2(x)
else y:= x*2^(d1-1)+rev2(floor(x/2));
fi;
B[y]:= 1;
od od:
B2:= Convolution(B, B);
A241491:= select(t -> B2[2*t-1] < 0.5, [$1..2^(N-1)]); # Robert Israel, Apr 24 2014
CROSSREFS
Cf. A006995, A261678 (values of 2n).
Sequence in context: A143846 A361105 A255226 * A356368 A068356 A215830
KEYWORD
nonn,base
AUTHOR
Robert Israel, Apr 24 2014
STATUS
approved