A293427 Squarefree numbers such that there are no adjacent 0's in their binary expansions.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 21, 22, 23, 26, 29, 30, 31, 42, 43, 46, 47, 53, 55, 58, 59, 61, 62, 85, 86, 87, 91, 93, 94, 95, 106, 107, 109, 110, 111, 118, 119, 122, 123, 127, 170, 173, 174, 181, 182, 183, 186, 187, 190, 191, 213, 214, 215, 218, 219, 221, 222, 223, 235, 237, 238, 239, 246, 247, 251, 253, 254, 255, 341

Offset: 1

Author

Antti Karttunen, Oct 11 2017

Keywords

• nonn
• base

Examples

			55 is present as 55 = 5*11 is squarefree (in A005117) and A007088(55) = 110111 does not contain two adjacent 0's. However, it is not present in A293430 because floor(55/2) = 27 is not a squarefree number.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Intersection of A003754 and A005117.

A293430 is a subsequence from which this differs for the first time at n=24, where a(24) = 55, a term not present in A293430.

Programs

Mathematica

Select[Range@ 360, And[SquareFreeQ@ #, SequenceCount[IntegerDigits[#, 2], {0, 0}] == 0] &] (* Michael De Vlieger, Oct 11 2017 *)

PARI

isA003754(n) = { n=bitor(n, n>>1)+1; n>>=valuation(n, 2); (n==1); }; \\ After Charles R Greathouse IV's Feb 06 2017 code.
n=1; k=1; while(k <= 10000, if(isA003754(n)&&issquarefree(n),write("b293427.txt", k, " ", n);k=k+1); n=n+1;); \\ Antti Karttunen, Oct 11 2017