cp's OEIS Frontend

A119377 Numbers k such that the next k binary digits of Pi are odd primes with no leading zeros.

%I A119377 #3 Mar 30 2012 17:31:18
%S A119377 2787,6,7,23,2,3,3,8,2,2,2,5,8,2,18,9,10,413,8,3,2,4019,14,4,2,2,11,
%T A119377 21,4,2,3,6,2,11,3,5,19,2,6,2,4,32,2,56,31,6,7,7,2,32,20,9,10,900,2,2,
%U A119377 2,97,5,2,8,64,3,13,3,2,6,7,15,3,2666,7,8,3,14,3,2,2,6,5,92,17,31,4,241,78,3
%N A119377 Numbers k such that the next k binary digits of Pi are odd primes with no leading zeros.
%C A119377 Partition the string of binary digits of Pi in such a way that each partition begins and ends with 1 (thus no leading or trailing zeros) and each such partition is prime.
%C A119377 Pi_2 = 1100100100001111110110101010001000100001011010001100001000..._2 (A004601).
%C A119377 If 2 is allowed as a member, then the sequence begins: 2787,2,5,6,2,2,2,39,5,8,2,18,9,10,2,153,2,6,2,18,7,7,12,2,2,2,2,....
%e A119377 a(1) represents the binary number 1100100100...(2767 terms)...0100000011 which equals the decimal number 7339860347...(819 terms)...8308318467 which is a prime.
%e A119377 a(2) represents the binary number 101001 which equals the decimal number 41, a prime.
%t A119377 ps = First@ RealDigits[Pi, 2, 12010]; lst = {}; Do[k = 1; While[fd = FromDigits[ Take[ps, k], 2]; EvenQ@fd || ps[[k + 1]] == 0 || !PrimeQ@fd, k++ ]; AppendTo[lst, k]; ps = Drop[ps, k], {n, 87}]; lst
%Y A119377 Cf. A004601, A068425, A117721, A065987, A119017.
%K A119377 base,nonn
%O A119377 1,1
%A A119377 _Robert G. Wilson v_, Jul 24 2006