login
A101121
Bitwise XOR of adjacent terms of A101120; also the nonzero terms of A101122.
3
7, 17, 34, 68, 159, 257, 514, 1028, 2063, 4097, 8194, 16388, 32831, 65537, 131074, 262148, 524303, 1048577, 2097154, 4194308, 8388639, 16777217, 33554434, 67108868, 134217743, 268435457, 536870914, 1073741828, 2147483775
OFFSET
1,1
COMMENTS
A101120 gives the records in A101119, which equals the nonzero differences of A006519 and A003484. A101122 is the XOR BINOMIAL transform of A101119 and has zeros everywhere except at positions equal to powers of 2.
FORMULA
a(n) = A101120(n-1) XOR A101120(n) for n>1, with a(1) = A101120(1), where A101120(n) = 2^(n+3) - 2^((n-1)(Mod 4)) - 8*floor((n+3)/4).
EXAMPLE
a(5) = 159 since A101120(4)=112, A101120(5)=239 and 159 = 112 XOR 239.
PROG
(PARI) {a(n)=bitxor(2^(n+2)-2^((n-2)%4)-8*((n+2)\4), 2^(n+3)-2^((n-1)%4)-8*((n+3)\4))}
(Python)
def A101121(n): return ((1<<(n+2))-(1<<((n-2)&3))-(((n+2)&-4)<<1))^((1<<(n+3))-(1<<((n-1)&3))-(((n+3)&-4)<<1)) # Chai Wah Wu, Jul 10 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Plouffe and Paul D. Hanna, Dec 02 2004
STATUS
approved