cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Simon Plouffe and Paul D. Hanna, Dec 02 2004

Keywords

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.

Examples

			a(5) = 159 since A101120(4)=112, A101120(5)=239 and 159 = 112 XOR 239.
		

Crossrefs

Programs

  • 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

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).