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%I #20 May 10 2020 23:09:00
%S 3,5,17,11,3,5,17,7,17,47,2,7,37,17,67,29,13,11,3,7,19,89,97,19,23,43,
%T 5,5,5,23,2,5,3,5,13,11,23,7,11,13,2,7,13,13,2,2,5,5,5,19,23,53,43,47,
%U 3,3,17,19,5,23,3,7,29,3,7,5,2,7,3,19,5,5,23,23,3,13,19,13,3,2,89,7,3,7,2,17,7,131,2,5,13,17,13,13,17,2,5,19,7,5,3,5,43,2
%N Sum s of consecutive digits of Pi such that s is prime.
%C A histogram of the first 1.4 million terms in this sequence reveals 7 as the most common term with a frequency of 15.25%. The smaller primes (2, 3, and 5) occur with frequencies between 12% and 14%, and larger primes rapidly decrease in frequency. 99% of the terms are composed of the first 20 primes (2, 3, 5, ..., 71). The largest of the first 1.4 million terms is a(220693) = 281, which is the sum of an otherwise prime-free sum of 64 consecutive digits of Pi (6 + 9 + 3 + 9 + 5 + 4 + 6 + 9 + 7 + 5 + 5 + 9 + 9 + 6 + 4 + 0 + 0 + 8 + 2 + 9 + 7 + 6 + 0 + 0 + 5 + 3 + 5 + 4 + 1 + 8 + 8 + 6 + 6 + 1 + 7 + 8 + 8 + 2 + 3 + 1+ 1 + 1 + 0 + 2 + 0 + 1 + 7 + 2 + 7 + 1 + 5 + 5 + 7 + 3 + 0 + 2 + 2 + 5 + 5 + 0 + 5 + 9 + 5 + 2).
%e a(1) = 3 because it is the first digit of Pi, and it is prime.
%e a(2) = 1 + 4 = 5 because it is the sum of the next consecutive digits of Pi, and it is prime, and the prior sum (1) is not prime.
%e a(3) = 1 + 5 + 9 + 2 = 17 because it is the sum of the next consecutive digits of Pi, and it is prime, and prior sums (1, 1 + 5 = 6, 1 + 5 + 9 = 15) are not prime.
%Y Cf. A000040, A000796.
%K nonn,base
%O 1,1
%A _Gil Broussard_, Aug 15 2014
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