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A033679 a(1) = 2; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

%I A033679 #13 Nov 22 2020 18:26:40
%S A033679 2,3,3,3,3,21,53,69,81,139,143,223,233,261,261,399,553,609,659,673,
%T A033679 1017,1187,1357,1571,1641,1839,2151,2191,2499,2511,2607,2667,2681,
%U A033679 3081,3351,4291,4319,4353,4489,4733,4819,6003,6011,6631,6797,7113,7429,7547,7651
%N A033679 a(1) = 2; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
%H A033679 Robert Israel, <a href="/A033679/b033679.txt">Table of n, a(n) for n = 1..300</a>
%p A033679 R:= 2,3: p:= 23: x:= 3:
%p A033679 for count from 3 to 100 do
%p A033679   for y from x by 2 do
%p A033679     if isprime(10^(1+ilog10(y))*p+y) then
%p A033679       R:= R, y; p:= 10^(1+ilog10(y))*p+y; x:= y;
%p A033679       break
%p A033679     fi
%p A033679 od od:
%p A033679 R; # _Robert Israel_, Nov 22 2020
%t A033679 a[1] = 2; 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 A033679 Cf. A069603, A074338, A033680, A033681, A046254, A046255, A046256, A046257, A046258, A046259, A111524.
%K A033679 nonn,base
%O A033679 1,1
%A A033679 _N. J. A. Sloane_
%E A033679 More terms from _Patrick De Geest_, May 15 1998
%E A033679 More terms from _Robert G. Wilson v_, Aug 05 2005