A241491 - OEIS

%I #8 Sep 04 2015 04:22:11

%S 88,94,104,121,122,155,262,314,328,368,377,397,416,431,433,434,440,

%T 466,472,497,500,590,620,654,655,664,671,676,688,704,710,716,720,905,

%U 945,961,973,977,1063,1103,1114,1131,1228,1234,1249,1250,1270,1312,1343,1348

%N 2*n is not the sum of two base-2 palindromes

%C Note that since all nonzero base-2 palindromes are odd, the sum of two nonzero base-2 palindromes is even.

%H Robert Israel, <a href="/A241491/b241491.txt">Table of n, a(n) for n = 1..10000</a>

%e 86 is not in the sequence because 2*86 = 7 + 165, and 7 and 165 are in A006995.

%p   N:= 15; # for all entries up to 2^(N-1)

%p with(SignalProcessing): # requires Maple 17+

%p rev2:= proc(n) option remember;

%p   rev2(floor(n/2)) + (n mod 2)*2^ilog2(n)

%p end;

%p rev2(0) := 0; rev2(1):= 1;

%p B:= Array(1..2^N,datatype=float[8]);

%p for d from 1 to N do

%p   d1:= ceil(d/2);

%p   for x from 2^(d1-1) to 2^d1-1 do

%p     if d::even then y:= x*2^d1+rev2(x)

%p     else y:= x*2^(d1-1)+rev2(floor(x/2));

%p     fi;

%p   B[y]:= 1;

%p od od:

%p B2:= Convolution(B,B);

%p A241491:= select(t -> B2[2*t-1] < 0.5, [$1..2^(N-1)]); # _Robert Israel_, Apr 24 2014

%Y Cf. A006995, A261678 (values of 2n).

%K nonn,base

%O 1,1

%A _Robert Israel_, Apr 24 2014