cp's OEIS Frontend

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

%I A101119 #19 Sep 08 2022 08:45:16
%S A101119 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,
%T A101119 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,
%U A101119 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
%N A101119 Nonzero differences of A006519 (highest power of 2 dividing n) and A003484 (Radon function).
%C A101119 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.
%H A101119 Antti Karttunen, <a href="/A101119/b101119.txt">Table of n, a(n) for n = 1..16384</a>
%F A101119 a(n) = A006519(16*n) - A003484(16*n) for n>=1. a(2*n-1) = 7 for n>=1.
%t A101119 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 *)
%o A101119 (PARI) {a(n)=2^valuation(16*n,2)-(8*(valuation(16*n,2)\4)+2^(valuation(16*n,2)%4))}
%o A101119 (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
%o A101119 (Python)
%o A101119 def A101119(n): return (1<<(m:=(~n&n-1).bit_length()+4))-((m&-4)<<1)-(1<<(m&3)) # _Chai Wah Wu_, Jul 10 2022
%Y A101119 Cf. A003484, A006519, A101120, A101122.
%K A101119 nonn
%O A101119 1,1
%A A101119 _Simon Plouffe_ and _Paul D. Hanna_, Dec 02 2004