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

1,1

Links

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

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

Example

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

Maple

P:= proc(q) local a, b, n;
for n from 1 to q do a:=convert(n, binary); b:=convert((n+1), binary);
print(convert(a+b*10^(ilog10(a)+1), decimal, binary)); od; end: P(100);
# alternative:
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 *)

Prog

(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 2nd 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

Crossrefs

Cf. A007088, A070939, A087737, A127423.

Sequence in context: A275809 A227793 A022139 * A143707 A306989 A003248

Adjacent sequences: A277348 A277349 A277350 * A277352 A277353 A277354

Keyword

nonn,base,easy

Author

Paolo P. Lava, Oct 10 2016

Status

approved