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
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
Programs
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Maple
f:= n -> (n+1)*2^(1+ilog2(n))+n: map(f, [$1..100]); # Robert Israel, Oct 14 2016
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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
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PARI
a(n) = (n+1)*2^(1+logint(n,2)) + n; \\ after Maple; Michel Marcus, Oct 15 2016
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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