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a(1) = 4; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
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%I #9 Jul 19 2015 00:36:28

%S 4,7,9,9,39,47,57,81,111,123,243,283,287,313,407,507,807,1057,1209,

%T 1211,1443,1447,1619,2019,2269,2429,2637,2679,2751,3007,3287,3789,

%U 3829,3833,3949,4151,4533,4821,5097,5331,5457,5529,5691,6021,6153,6393,6409

%N a(1) = 4; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

%t a[1] = 4; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k ++ ]; k]; Table[ a[n], {n, 47}] (* _Robert G. Wilson v_, Aug 05 2005 *)

%Y Cf. A069606, A074340, A033680, A033679, A033681, A046255, A046256, A046257, A046258, A046259, A111524.

%K nonn

%O 1,1

%A _Patrick De Geest_, May 15 1998