A277351 Value of (n+1,n) concatenated in binary representation.

5, 14, 19, 44, 53, 62, 71, 152, 169, 186, 203, 220, 237, 254, 271, 560, 593, 626, 659, 692, 725, 758, 791, 824, 857, 890, 923, 956, 989, 1022, 1055, 2144, 2209, 2274, 2339, 2404, 2469, 2534, 2599, 2664, 2729, 2794, 2859, 2924, 2989, 3054, 3119, 3184, 3249, 3314

Offset: 1

Author

Paolo P. Lava, Oct 10 2016

Keywords

• nonn
• base
• easy

Examples

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

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007088, A070939, A087737, A127423.

Programs

Maple

f:= n -> (n+1)*2^(1+ilog2(n))+n:
map(f, [$1..100]); # Robert Israel, Oct 14 2016

Mathematica

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

PARI

a(n) = subst(Pol(concat(binary(n+1), binary(n))), x, 2); \\ Michel Marcus, Oct 10 2016

PARI

a(n) = (n+1)*2^(1+logint(n,2)) + n; \\ after Maple; Michel Marcus, Oct 15 2016

Python

def a(n): return int(bin(n+1)[2:] + bin(n)[2:], 2)
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, May 14 2021

Formula

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

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