A265885 a(n) = n IMPL prime(n), where IMPL is the bitwise logical implication.

2, 3, 5, 7, 11, 13, 25, 23, 23, 29, 31, 55, 59, 59, 63, 63, 63, 61, 111, 111, 107, 111, 123, 127, 103, 101, 103, 107, 111, 113, 127, 223, 223, 223, 221, 223, 223, 251, 255, 255, 247, 245, 255, 211, 215, 215, 211, 223, 239, 237, 237, 239, 251, 251, 457, 455

Offset: 1

Author

Reinhard Zumkeller, Dec 17 2015

Keywords

• nonn

Examples

			.   prime(25)=97 | 1100001
.             25 |   11001
.   -------------+--------
.     25 IMPL 97 | 1100111 -> a(25) = 103 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Implies

Crossrefs

Cf. A000040, A004676, A007088, A070883 (XOR), A265705.

Programs

Haskell

a265885 n = n `bimpl` a000040 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

Julia

using IntegerSequences
[Bits("IMP", n, p) for (n, p) in enumerate(Primes(1, 263))] |> println  # Peter Luschny, Sep 25 2021

Maple

a:= n-> Bits[Implies](n, ithprime(n)):
seq(a(n), n=1..56);  # Alois P. Heinz, Sep 24 2021

Mathematica

IMPL[n_, k_] := If[n == 0, 0, BitOr[2^Length[IntegerDigits[k, 2]]-1-n, k]];
a[n_] := n ~IMPL~ Prime[n];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 25 2021, after David A. Corneth's code in A265705 *)

PARI

a(n) = bitor((2<Michel Marcus, Jan 22 2022

Formula

a(n) = A265705(A000040(n),n).