A003484 -id:A003484 - cp's OEIS frontend

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

Simon Plouffe and Paul D. Hanna, Dec 02 2004

nonn

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.

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

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

{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))}

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

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).

A279170 a(n) is the smallest among the natural numbers m with the property that there exists a non-constant quadratic map S^n -> S^m from the n-dimensional sphere to the m-dimensional sphere.

Original entry on oeis.org

1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24, 24, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 40, 40, 40, 40, 40, 40, 48, 48, 48, 48, 48, 48, 48, 48, 48, 56, 56, 56, 56, 56, 56, 56, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 72, 72, 72, 72, 80, 80, 80, 80, 80, 80, 80, 80, 80, 88, 88, 88, 88, 88, 88, 88, 96, 96, 96, 96, 96

Offset: 1

Mamuka Jibladze, Dec 07 2016

nonn

Coincides with A053644 until n=24.

P. Yiu, Quadratic Forms between Euclidean Spheres, Manuscripta Math. 83, pp. 171-181 (1994).

A003484 used in the definition. Cf. A053644.

Uniquely determined by the following: a(2^t + m) = 2^t if 0 <= m < A003484(2^t); a(2^t + m) = 2^t + a(m) if A003484(2^t) <= m < 2^t.

cp's OEIS Frontend

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

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