A265885 - OEIS

%I #17 Jan 22 2022 09:39:19

%S 2,3,5,7,11,13,25,23,23,29,31,55,59,59,63,63,63,61,111,111,107,111,

%T 123,127,103,101,103,107,111,113,127,223,223,223,221,223,223,251,255,

%U 255,247,245,255,211,215,215,211,223,239,237,237,239,251,251,457,455

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

%H Reinhard Zumkeller, <a href="/A265885/b265885.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Implies.html">Implies</a>

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

%e .   prime(25)=97 | 1100001

%e .             25 |   11001

%e .   -------------+--------

%e .     25 IMPL 97 | 1100111 -> a(25) = 103 .

%p a:= n-> Bits[Implies](n, ithprime(n)):

%p seq(a(n), n=1..56);  # _Alois P. Heinz_, Sep 24 2021

%t IMPL[n_, k_] := If[n == 0, 0, BitOr[2^Length[IntegerDigits[k, 2]]-1-n, k]];

%t a[n_] := n ~IMPL~ Prime[n];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Sep 25 2021, after _David A. Corneth_'s code in A265705 *)

%o (Haskell)

%o a265885 n = n `bimpl` a000040 n where

%o    bimpl 0 0 = 0

%o    bimpl p q = 2 * bimpl p' q' + if u <= v then 1 else 0

%o                where (p', u) = divMod p 2; (q', v) = divMod q 2

%o (Julia)

%o using IntegerSequences

%o [Bits("IMP", n, p) for (n, p) in enumerate(Primes(1, 263))] |> println  # _Peter Luschny_, Sep 25 2021

%o (PARI) a(n) = bitor((2<<logint(prime(n), 2))-1-n, prime(n)); \\ _Michel Marcus_, Jan 22 2022

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 17 2015