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A265885
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a(n) = n IMPL prime(n), where IMPL is the bitwise logical implication.
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3
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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
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listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Implies
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FORMULA
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EXAMPLE
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. prime(25)=97 | 1100001
. 25 | 11001
. -------------+--------
. 25 IMPL 97 | 1100111 -> a(25) = 103 .
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MAPLE
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a:= n-> Bits[Implies](n, ithprime(n)):
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MATHEMATICA
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IMPL[n_, k_] := If[n == 0, 0, BitOr[2^Length[IntegerDigits[k, 2]]-1-n, k]];
a[n_] := n ~IMPL~ Prime[n];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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