OFFSET
0,2
COMMENTS
These are the indices n for which A034798(n) = 0.
From Antti Karttunen, Jan 30 2014: (Start)
A236678(a(n)) = n+1 for all n.
Differs from A047467 for the first time at a(64).
Differs from A126002(n+1) for the first time not later than at n=281474976710656 (= 2^48), as:
a((2^48)-1) = a(281474976710655) = 18085043209519168250 < 18446744073709551616 (= 2^64), while
a(2^48) = a(281474976710656) = 36893488147419103232 > 2^64.
(End)
REFERENCES
J. H. Conway, On numbers and games.
LINKS
FORMULA
a(0) = 0; a(n+1) = least x > a(n) such that the coefficient of 2^a(j) is zero in the binary expansion of x for all j < n+1
Alternatively: rewrite the binary representation of n in such a way that the forbidden bit-positions given by this sequence (with bit-position 0 standing for the least significant bit) are vacated, by shifting the rest of bits one bit left. E.g., bit-positions 0, 2, 8, 10, ... are forbidden, thus we rewrite 1 to 1x = 10 = 2, 2 (in binary 10) to 1x0x = 1000 = 8, 3 (in binary 11) to 1x1x = 1010 = 10, 4 (in binary 100) to 10x0x = 1000 = 16, 64 (in binary 1000000) to 1x00000x0x = 1000000000 = 512, etc. - Antti Karttunen, Jan 30 2014
EXAMPLE
a(1) = 2 (rather than 1) because 1 = 2^0 = 2^a(0); a(64) = 512 (rather than 256) because 256 = 2^8 = 2^a(2).
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Rob Arthan, Jan 28 2003
EXTENSIONS
More terms from Antti Karttunen, Jan 29 2014
STATUS
approved