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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A051411 A195016 A296553 * A212117 A160635 A339527
KEYWORD
nonn
AUTHOR
Simon Plouffe and Paul D. Hanna, Dec 02 2004
STATUS
approved

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Last modified July 12 19:59 EDT 2024. Contains 374252 sequences. (Running on oeis4.)