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

1,1

Comments

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

Links

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

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

Adjacent sequences: A241488 A241489 A241490 * A241492 A241493 A241494

Keyword

nonn,base

Author

Robert Israel, Apr 24 2014

Status

approved