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a(1) = 23. Later primes are determined by the rule that the digits of the sequence specify the lengths of the terms. The smallest prime with the specified number of digits is used each time.
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%I #2 Mar 31 2012 13:46:51

%S 23,113,2,2,113,11,11,2,2,113,2,2,2,2,11,11,2,2,113,11,11,11,11,2,2,2,

%T 2,11,11,2,2,113,2,2,2,2,2,2,2,2,11,11,11,11,2,2,2,2,11,11,2,2,113,11,

%U 11,11,11,11,11,11,11,2,2,2,2,2,2,2,2,11,11,11,11,2,2,2,2,11,11,2,2,113

%N a(1) = 23. Later primes are determined by the rule that the digits of the sequence specify the lengths of the terms. The smallest prime with the specified number of digits is used each time.

%e The first prime has 2 digits, the next one 3, the next one 1, then 1, 3, 2, 2, 1, 1, 3 etc. The sequence of digits specifies the sequence.

%K base,easy,nonn

%O 1,1

%A _Eric Angelini_, Jan 27 2005