A164563 A positive integer n is included if the distinct odd numerical values of substrings in the binary representation of n are all coprime to each other.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 23, 24, 26, 28, 29, 32, 33, 34, 35, 36, 37, 40, 41, 42, 44, 46, 48, 49, 52, 56, 58, 64, 65, 66, 68, 69, 70, 72, 73, 74, 80, 81, 82, 84, 88, 92, 96, 98, 104, 112, 116, 128, 129, 130, 131, 132, 133, 136, 137, 138, 140, 144, 145

Offset

1,2

Comments

From Robert Israel, Aug 04 2019: (Start)

n is in the sequence if and only if 2*n is in the sequence.

Contains 2^k+1 for all k. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..2500

Example

27 in binary is 11011. The substrings of this, each with a distinct odd numerical value, (and their decimal equivalents) are 1 (1), 11 (3), 101 (5), 1011 (11), 1101 (13), 11011 (27). Since 3 is not coprime to 27, then 27 is not in this sequence.
However, 21 in binary is 10101. The distinct odd substrings are 1, 101 (5), and 10101 (21). Since 1, 5, and 21 are all coprime to each other, then 21 is in this sequence.

Maple

f:= proc(n) local L, J, S, i, j, k;
  L:= convert(n, base, 2);
  J:= select(t -> L[t]=1, [$1..nops(L)]);
  S:= map(t -> add(2^(k-1)*t[k], k=1..nops(t)), {seq(seq(L[J[i]..J[j]], i=1..j), j=1..nops(J))});
  ilcm(op(S))=convert(S, `*`)
end proc:
select(f, [$1..300]); # Robert Israel, Aug 04 2019

Crossrefs

A164564

Sequence in context: A325044 A343822 A303550 * A179892 A348519 A061773

Adjacent sequences: A164560 A164561 A164562 * A164564 A164565 A164566

Keyword

base,nonn

Author

Leroy Quet, Aug 16 2009

Extensions

More terms from Zak Seidov, Aug 17 2009

Corrected by Robert Israel, Aug 04 2019

Status

approved