cp's OEIS Frontend

A333649 Numbers k such that the second k binary digits of Pi represent a prime (leading zeros allowed).

%I A333649 #20 Dec 17 2024 10:35:35
%S A333649 3,7,41,93,166,316,1449,6605,10015,13097,16284,19075,35137,70558,
%T A333649 128436
%N A333649 Numbers k such that the second k binary digits of Pi represent a prime (leading zeros allowed).
%C A333649 Numbers k such that floor(2^(2*k-2)*Pi) mod 2^k is prime.
%C A333649 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.
%C A333649 a(16) > 2*10^5. - _Michael S. Branicky_, Dec 17 2024
%e A333649 a(2) = 7 is a term 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.
%p A333649 L:= floor(Pi*2^19998):
%p A333649 select(n -> isprime(floor(L*2^(2*n-20000)) mod 2^n), [$1..10000]);
%o A333649 (PARI) default(realprecision, 10^5);
%o A333649 is(k) = ispseudoprime(floor(4^(k-1)*Pi)%2^k); \\ _Jinyuan Wang_, Mar 31 2020
%Y A333649 Cf. A004601, A065987.
%K A333649 nonn,base,more
%O A333649 1,1
%A A333649 _Robert Israel_, Mar 31 2020
%E A333649 a(9) from _Jinyuan Wang_, Mar 31 2020
%E A333649 a(10)-a(13) from _Chai Wah Wu_, Apr 06 2020
%E A333649 a(14)-a(15) from _Michael S. Branicky_, Dec 16 2024