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Numbers n such that the first n quaternary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).
12

%I #14 Apr 07 2020 19:49:07

%S 1,2,3,5,10,19,72,115,220,315,375,12408

%N Numbers n such that the first n quaternary 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 4, omit the decimal point and look for prefixes in the resulting string which form base-4 primes.

%C Numbers n such that A065838(n) is prime.

%C The next term in the sequence, if it exists, is greater than 10000. - _Nathaniel Johnston_, Nov 15 2010

%e E.g., the first a(5) or 10 quaternary digits of Pi are 31.12332323{4} and 3112332323{4} is the prime 880571{10}.

%t p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 || p[[ # ]] == 2 || p[[ # ]] == 3 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 4]], Print[ n]], {n, 1, 4000} ]

%Y Cf. A065828 up to A065839, A000796, A011545, A011546, A055145, A005042, A060421, A039954, A048796.

%K nonn,base,hard

%O 1,2

%A _Patrick De Geest_, Nov 24 2001

%E a(12) from _Chai Wah Wu_, Apr 07 2020