A277351 - OEIS

%I #27 Jan 06 2025 20:02:15

%S 5,14,19,44,53,62,71,152,169,186,203,220,237,254,271,560,593,626,659,

%T 692,725,758,791,824,857,890,923,956,989,1022,1055,2144,2209,2274,

%U 2339,2404,2469,2534,2599,2664,2729,2794,2859,2924,2989,3054,3119,3184,3249,3314

%N Value of (n+1,n) concatenated in binary representation.

%H Paolo P. Lava, <a href="/A277351/b277351.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (n+1) * 2^A070939(n) + n.

%F G.f.: (1-x)^(-2)*(5*x - 2*x^2 + Sum_{m>=1} ((2^(2*m)+2^m)*x^(2^m) - 2^(2*m)*x^(2^m+1))). - _Robert Israel_, Oct 14 2016

%e Binary representation of 12 and 13 are 1100 and 1101. Then, concat(1101,1100) = 11011100 converted in decimal representation is 220.

%p f:= n -> (n+1)*2^(1+ilog2(n))+n:

%p map(f, [$1..100]); # _Robert Israel_, Oct 14 2016

%t Table[FromDigits[Join @@ Map[IntegerDigits[#, 2] &, {n + 1, n}], 2], {n, 50}] (* _Michael De Vlieger_, Oct 14 2016 *)

%o (PARI) a(n) = subst(Pol(concat(binary(n+1), binary(n))), x, 2); \\ _Michel Marcus_, Oct 10 2016

%o (PARI) a(n) = (n+1)*2^(1+logint(n,2)) + n; \\ after 2nd Maple; _Michel Marcus_, Oct 15 2016

%o (Python)

%o def a(n): return int(bin(n+1)[2:] + bin(n)[2:], 2)

%o print([a(n) for n in range(1, 51)]) # _Michael S. Branicky_, May 14 2021

%Y Cf. A007088, A070939, A087737, A127423.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Oct 10 2016