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

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

Author

Robert Israel, Apr 24 2014

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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