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A293427
Squarefree numbers such that there are no adjacent 0's in their binary expansions.
2
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
1,2
EXAMPLE
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.
MATHEMATICA
Select[Range@ 360, And[SquareFreeQ@ #, SequenceCount[IntegerDigits[#, 2], {0, 0}] == 0] &] (* Michael De Vlieger, Oct 11 2017 *)
PROG
(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
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.
Sequence in context: A047586 A103841 A003754 * A293430 A087006 A345297
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Oct 11 2017
STATUS
approved