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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Implies

Formula

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

Example

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

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 *)

Prog

(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
(PARI) a(n) = bitor((2<<logint(prime(n), 2))-1-n, prime(n)); \\ Michel Marcus, Jan 22 2022

Crossrefs

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

Sequence in context: A343973 A024694 A024320 * A294994 A292205 A111252

Adjacent sequences: A265882 A265883 A265884 * A265886 A265887 A265888

Keyword

nonn

Author

Reinhard Zumkeller, Dec 17 2015

Status

approved