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

%I A265885 #18 Feb 16 2025 08:33:28
%S A265885 2,3,5,7,11,13,25,23,23,29,31,55,59,59,63,63,63,61,111,111,107,111,
%T A265885 123,127,103,101,103,107,111,113,127,223,223,223,221,223,223,251,255,
%U A265885 255,247,245,255,211,215,215,211,223,239,237,237,239,251,251,457,455
%N A265885 a(n) = n IMPL prime(n), where IMPL is the bitwise logical implication.
%H A265885 Reinhard Zumkeller, <a href="/A265885/b265885.txt">Table of n, a(n) for n = 1..10000</a>
%H A265885 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Implies.html">Implies</a>
%F A265885 a(n) = A265705(A000040(n),n).
%e A265885 .   prime(25)=97 | 1100001
%e A265885 .             25 |   11001
%e A265885 .   -------------+--------
%e A265885 .     25 IMPL 97 | 1100111 -> a(25) = 103 .
%p A265885 a:= n-> Bits[Implies](n, ithprime(n)):
%p A265885 seq(a(n), n=1..56);  # _Alois P. Heinz_, Sep 24 2021
%t A265885 IMPL[n_, k_] := If[n == 0, 0, BitOr[2^Length[IntegerDigits[k, 2]]-1-n, k]];
%t A265885 a[n_] := n ~IMPL~ Prime[n];
%t A265885 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Sep 25 2021, after _David A. Corneth_'s code in A265705 *)
%o A265885 (Haskell)
%o A265885 a265885 n = n `bimpl` a000040 n where
%o A265885    bimpl 0 0 = 0
%o A265885    bimpl p q = 2 * bimpl p' q' + if u <= v then 1 else 0
%o A265885                where (p', u) = divMod p 2; (q', v) = divMod q 2
%o A265885 (Julia)
%o A265885 using IntegerSequences
%o A265885 [Bits("IMP", n, p) for (n, p) in enumerate(Primes(1, 263))] |> println  # _Peter Luschny_, Sep 25 2021
%o A265885 (PARI) a(n) = bitor((2<<logint(prime(n), 2))-1-n, prime(n)); \\ _Michel Marcus_, Jan 22 2022
%Y A265885 Cf. A000040, A004676, A007088, A070883 (XOR), A265705.
%K A265885 nonn
%O A265885 1,1
%A A265885 _Reinhard Zumkeller_, Dec 17 2015