A101121 Bitwise XOR of adjacent terms of A101120; also the nonzero terms of A101122.

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.

Links

Table of n, a(n) for n=1..29.

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

Cf. A003484, A006519, A101119, A101120, A101122.

Sequence in context: A051411 A195016 A296553 * A212117 A160635 A339527

Adjacent sequences: A101118 A101119 A101120 * A101122 A101123 A101124

Keyword

nonn

Author

Simon Plouffe and Paul D. Hanna, Dec 02 2004

Status

approved