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A241491 2*n is not the sum of two base-2 palindromes.

%I A241491 #10 Jul 23 2025 11:14:39
%S A241491 88,94,104,121,122,155,262,314,328,368,377,397,416,431,433,434,440,
%T A241491 466,472,497,500,590,620,654,655,664,671,676,688,704,710,716,720,905,
%U A241491 945,961,973,977,1063,1103,1114,1131,1228,1234,1249,1250,1270,1312,1343,1348
%N A241491 2*n is not the sum of two base-2 palindromes.
%C A241491 Note that since all nonzero base-2 palindromes are odd, the sum of two nonzero base-2 palindromes is even.
%H A241491 Robert Israel, <a href="/A241491/b241491.txt">Table of n, a(n) for n = 1..10000</a>
%e A241491 86 is not in the sequence because 2*86 = 7 + 165, and 7 and 165 are in A006995.
%p A241491   N:= 15; # for all entries up to 2^(N-1)
%p A241491 with(SignalProcessing): # requires Maple 17+
%p A241491 rev2:= proc(n) option remember;
%p A241491   rev2(floor(n/2)) + (n mod 2)*2^ilog2(n)
%p A241491 end;
%p A241491 rev2(0) := 0; rev2(1):= 1;
%p A241491 B:= Array(1..2^N,datatype=float[8]);
%p A241491 for d from 1 to N do
%p A241491   d1:= ceil(d/2);
%p A241491   for x from 2^(d1-1) to 2^d1-1 do
%p A241491     if d::even then y:= x*2^d1+rev2(x)
%p A241491     else y:= x*2^(d1-1)+rev2(floor(x/2));
%p A241491     fi;
%p A241491   B[y]:= 1;
%p A241491 od od:
%p A241491 B2:= Convolution(B,B);
%p A241491 A241491:= select(t -> B2[2*t-1] < 0.5, [$1..2^(N-1)]); # _Robert Israel_, Apr 24 2014
%Y A241491 Cf. A006995, A261678 (values of 2n).
%K A241491 nonn,base
%O A241491 1,1
%A A241491 _Robert Israel_, Apr 24 2014