A190784 Numbers whose binary representation is a substring of the concatenation of the binary representation of all smaller nonnegative integers not listed earlier, taken in decreasing order.

2, 6, 7, 9, 11, 12, 14, 17, 19, 20, 21, 22, 25, 26, 27, 28, 29, 30, 31, 33, 34, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 65, 67, 69, 71, 72, 73, 74, 77, 78, 80, 81, 82, 84, 86, 87, 89, 90, 92, 93, 94

Offset

1,1

Comments

Also, nonnegative integers which do not occur in A118250.

Up to the reversed (decreasing) order of concatenation, a binary analog of Hannah Rollman's numbers A048992.

Links

Table of n, a(n) for n=1..65.

Example

The binary representation of 2="10"[2] is a substring of the concatenation of 1 and 0, therefore a(1)=2. This term a(1)=2="10" will henceforth be excluded from the concatenations considered in the sequel.
The binary representations of 3, 4 and 5 are not a substrings of concat("1", "0") resp. concat("11", "1", "0") resp. concat("100", "11", "1", "0"). (Note that 2="10" is not among the concatenated numbers.)
But 6="110"[2] is again a substring of concat(5="101", 4="100", 3="11", "1", "0"), therefore a(2)=6. In the sequel, a(2)=6="110" will now also be always excluded from the concatenations, as is a(1)=2.

Crossrefs

Analog of A128291 for the "with reversal" variant A118250 of A118248.

Cf. A048991, A048992.

Sequence in context: A206446 A079335 A278999 * A344167 A061416 A190247

Adjacent sequences: A190781 A190782 A190783 * A190785 A190786 A190787

Keyword

nonn,base

Author

M. F. Hasler, Dec 29 2012

Status

approved