A265716 a(n) = n IMPL (2*n), where IMPL is the bitwise logical implication.

0, 2, 5, 6, 11, 10, 13, 14, 23, 22, 21, 22, 27, 26, 29, 30, 47, 46, 45, 46, 43, 42, 45, 46, 55, 54, 53, 54, 59, 58, 61, 62, 95, 94, 93, 94, 91, 90, 93, 94, 87, 86, 85, 86, 91, 90, 93, 94, 111, 110, 109, 110, 107, 106, 109, 110, 119, 118, 117, 118, 123, 122

Offset

0,2

Comments

The scatterplot exhibits fractal qualities. - Bill McEachen, Dec 27 2022

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..8191 <= 2^13-1

Eric Weisstein's World of Mathematics, Implies

Formula

a(n) = A265705(2*n,n): central terms of triangle A265705;

a(A247648(n)) = 2*A247648(n).

a(n)= bitor(A003817(n)-n, 2*n) (conjectured). - Bill McEachen, Dec 13 2021

2n <= a(n) <= 3n. - Charles R Greathouse IV, Jan 20 2023

Example

.      2*21=42 | 101010                      2*6=12 | 1100
.           21 |  10101                           6 |  110
.   -----------+-------                   ----------+-----
.   21 IMPL 42 | 101010 -> a(21) = 42     6 IMPL 12 | 1101 -> a(6) = 13 .

Maple

A265716 := n -> Bits:-Implies(n, 2*n):
seq(A265716(n), n=0..61); # Peter Luschny, Sep 23 2019

Mathematica

IMPL[n_, k_] := If[n == 0, 0, BitOr[2^Length[IntegerDigits[k, 2]]-1-n, k]];
a[n_] := n ~IMPL~ (2n);
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 16 2021 *)

Prog

(Haskell)
a265716 n = n `bimpl` (2 * n) where
   bimpl 0 0 = 0
   bimpl p q = 2 * bimpl p' q' + if u <= v then 1 else 0
               where (p', u) = divMod p 2; (q', v) = divMod q 2
(PARI) a(n)=bitor(bitneg(n, exponent(n)+1), 2*n) \\ Charles R Greathouse IV, Jan 20 2023

Crossrefs

Cf. A265705, A247648, A003817.

Sequence in context: A160645 A248616 A341522 * A206332 A269966 A026344

Adjacent sequences: A265713 A265714 A265715 * A265717 A265718 A265719

Keyword

nonn,look,easy

Author

Reinhard Zumkeller, Dec 15 2015

Status

approved