cp's OEIS Frontend

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.

A036556 Integers which when multiplied by 3 have an odd number of 1's in their binary expansion (cf. A000069).

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%I A036556 #25 Aug 06 2023 03:05:57
%S A036556 7,14,23,27,28,29,31,39,46,54,56,57,58,62,71,78,87,91,92,93,95,103,
%T A036556 107,108,109,111,112,113,114,115,116,117,119,123,124,125,127,135,142,
%U A036556 151,155,156,157,159,167,174,182,184,185,186,190,199,206,214
%N A036556 Integers which when multiplied by 3 have an odd number of 1's in their binary expansion (cf. A000069).
%C A036556 In other words, numbers n such that 3n is odious.
%C A036556 Numbers n such that valuation(binomial(3n,n),2) is odd. - _Benoit Cloitre_, Jun 06 2004
%C A036556 Intersection of A000069 and A008585 (multiples of 3), divided by 3.
%H A036556 G. C. Greubel, <a href="/A036556/b036556.txt">Table of n, a(n) for n = 1..10000</a>
%F A036556 a(n) = A180963(n)/3. - _Amiram Eldar_, Aug 06 2023
%t A036556 Select[ Range[ 214 ], OddQ[ Plus@@IntegerDigits[ 3#, 2 ]]& ]
%o A036556 (PARI) for(n=1,214,if(valuation(binomial(3*n,n),2)%2==1,print1(n,","))) \\ _Benoit Cloitre_, Jun 06 2004
%o A036556 (Magma) [ n : n in [0..150] | IsOdd(&+Intseq(3*n, 2))]; // _Vincenzo Librandi_, Apr 13 2011
%Y A036556 Cf. A000069, A036555, A036557, A180963.
%K A036556 nonn,base
%O A036556 1,1
%A A036556 _Dan Hoey_
%E A036556 Definition corrected by _N. J. A. Sloane_, Jan 09 2007