A101119 Nonzero differences of A006519 (highest power of 2 dividing n) and A003484 (Radon function).

7, 22, 7, 52, 7, 22, 7, 112, 7, 22, 7, 52, 7, 22, 7, 239, 7, 22, 7, 52, 7, 22, 7, 112, 7, 22, 7, 52, 7, 22, 7, 494, 7, 22, 7, 52, 7, 22, 7, 112, 7, 22, 7, 52, 7, 22, 7, 239, 7, 22, 7, 52, 7, 22, 7, 112, 7, 22, 7, 52, 7, 22, 7, 1004, 7, 22, 7, 52, 7, 22, 7, 112, 7, 22, 7, 52, 7, 22, 7, 239

Offset

1,1

Comments

A006519 and A003484 differ only at every 16th term; this sequence forms the nonzero differences. Records form A101120. Equals the XOR BINOMIAL transform of A101122.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A006519(16*n) - A003484(16*n) for n>=1. a(2*n-1) = 7 for n>=1.

Mathematica

Table[2^(IntegerExponent[16*n, 2]) - 8*Floor[IntegerExponent[16*n, 2]/4] - 2^(Mod[IntegerExponent[16*n, 2], 4]), {n, 1, 50}] (* G. C. Greubel, Nov 01 2018 *)

Prog

(PARI) {a(n)=2^valuation(16*n, 2)-(8*(valuation(16*n, 2)\4)+2^(valuation(16*n, 2)%4))}
(Magma) [2^Valuation(16*n, 2) - 8*Floor(Valuation(16*n, 2)/4) - 2^(Valuation(16*n, 2) mod 4): n in [1..50]]; // G. C. Greubel, Nov 01 2018
(Python)
def A101119(n): return (1<<(m:=(~n&n-1).bit_length()+4))-((m&-4)<<1)-(1<<(m&3)) # Chai Wah Wu, Jul 10 2022

Crossrefs

Cf. A003484, A006519, A101120, A101122.

Sequence in context: A213152 A082826 A130740 * A217014 A200886 A070412

Adjacent sequences: A101116 A101117 A101118 * A101120 A101121 A101122

Keyword

nonn

Author

Simon Plouffe and Paul D. Hanna, Dec 02 2004

Status

approved