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.
%I A324465 #32 Jul 10 2022 16:11:11 %S A324465 0,0,1,3,2,2,3,5,2,3,4,6,5,4,5,7,2,3,4,6,5,5,6,8,5,6,7,9,8,6,7,9,2,3, %T A324465 4,6,5,5,6,8,5,6,7,9,8,7,8,10,5,6,7,9,8,8,9,11,8,9,10,12,11,8,9,11,2, %U A324465 3,4,6,5,5,6,8,5,6,7,9,8,7,8,10,5,6,7,9 %N A324465 Exponent of highest power of 2 that divides A324152(n). %C A324465 First occurrence of k=0,1,2,...: 0, 2, 4, 3, 10, 7, 11, 15, 23, 27, 47, 55, 59, 111, 119, 123, 239, 247, 251, 495, 503, 507, 1007, 1015, 1019, 2031, 2039, 2043, 4079, 4087, 4091, 8175, 8183, 8187, 16367, 16375, 16379, 32751, 32759, 32763, 65519, 65527, 65531, 131055, 131063, 131067, ..., . _Robert G. Wilson v_, Mar 01 2019 %H A324465 Robert G. Wilson v, <a href="/A324465/b324465.txt">Table of n, a(n) for n = 0..10000</a> (first 501 terms from N. J. A. Sloane) %F A324465 a(n) = 3*wt(n) - (2-adic valuation of (n+1)*(n+2)*(n+3)) %F A324465 = 3*A000120(n) - (A007814(n+1)+A007814(n+2)+A007814(n+3)). %F A324465 E.g. if n = 14 = 1110_2, with weight 3, we get a(14) = 3*3 - 2-adic valuation of 15*16*17 = 9 - 4 = 5. %t A324465 f[n_] := IntegerExponent[(3/((n + 1)(n + 2)(n + 3)))*Multinomial[n, n, n, n], 2]; f[0] = 0; Array[f, 84, 0] (* _Robert G. Wilson v_, Mar 01 2019 *) %o A324465 (Python 3.10+) %o A324465 def A324465(n): return 3*n.bit_count()-(~(n+1)&n).bit_length()-(~(n+2)&n+1).bit_length()-(~(n+3)&n+2).bit_length() if n else 0 # _Chai Wah Wu_, Jul 10 2022 %o A324465 (PARI) a(n) = 3*hammingweight(n) - valuation((n+1)*(n+2)*(n+3), 2); \\ _Michel Marcus_, Jul 10 2022 %Y A324465 Cf. A000120 (binary weight), A007814, A324152, A324467. %K A324465 nonn %O A324465 0,4 %A A324465 _N. J. A. Sloane_, Mar 01 2019