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

Author

Reinhard Zumkeller, Dec 15 2015

Keywords

• nonn
• look
• easy

Comments

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

Examples

			.      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 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..8191 <= 2^13-1
• Eric Weisstein's World of Mathematics, Implies

Crossrefs

Cf. A265705, A247648, A003817.

Programs

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

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 *)

PARI

a(n)=bitor(bitneg(n, exponent(n)+1), 2*n) \\ Charles R Greathouse IV, Jan 20 2023

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