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%I #13 Apr 07 2020 08:50:27
%S 2,4,10,24,29,34,43,62,76,351,778,2736,4992,7517,22044,40390
%N Numbers k such that the first k binary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).
%C In other words, take the decimal expansion of Pi, drop any digits greater than 1, omit the decimal point and look for prefixes in the resulting string which form base-2 primes.
%C Numbers k such that A065830(k) is prime.
%e The first a(3)=10 binary digits of Pi are 1101110001_2 which is prime 881_10.
%t p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 2]], Print[n]], {n, 1, Length[p] } ]
%Y Cf. A065828 up to A065840, A000796, A011545, A011546, A055143, A005042, A060421, A039954, A048796.
%K nonn,base,hard,more
%O 1,1
%A _Patrick De Geest_, Nov 24 2001
%E More terms from _Robert G. Wilson v_, Nov 30 2001
%E a(15)-a(16) from _Chai Wah Wu_, Apr 06 2020
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