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A277351 Value of (n+1,n) concatenated in binary representation. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified December 10 20:48 EST 2019. Contains 329909 sequences. (Running on oeis4.)