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A333649
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Numbers k such that the second k binary digits of Pi represent a prime (leading zeros allowed).
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0
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3, 7, 41, 93, 166, 316, 1449, 6605, 10015, 13097, 16284, 19075, 35137
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OFFSET
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1,1
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COMMENTS
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Numbers k such that floor(2^(2*k-2)*Pi) mod 2^k is prime.
A random number of k binary digits has probability ~ constant/k of being prime, so heuristically we should expect the sequence to be infinite, but growing exponentially.
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LINKS
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EXAMPLE
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a(2)=7 is in the sequence because the first 14 binary digits in Pi are 11.001001000011; the second 7 binary digits are 1000011, or 67 in decimal, which is prime.
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MAPLE
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L:= floor(Pi*2^19998):
select(n -> isprime(floor(L*2^(2*n-20000)) mod 2^n), [$1..10000]);
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PROG
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(PARI) default(realprecision, 10^5);
is(k) = ispseudoprime(floor(4^(k-1)*Pi)%2^k); \\ Jinyuan Wang, Mar 31 2020
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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