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

Author

Simon Plouffe and Paul D. Hanna, Dec 02 2004

Keywords

• nonn

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

Crossrefs

Cf. A003484, A006519, A101120, A101122.

Programs

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

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 *)

PARI

{a(n)=2^valuation(16*n,2)-(8*(valuation(16*n,2)\4)+2^(valuation(16*n,2)%4))}

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

Formula

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