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A241845 a(1)=1; for n >1 a(n) is the smallest prime divisor of the number obtained from concatenation of 1 and the first n-1 composites.

%I A241845 #20 Jul 27 2021 18:27:27
%S A241845 1,2,2,2,37,2,2,2,5,2,2,2,27793,2,2,3,2,29,2,2,2,19,2,5,2,2,
%T A241845 1468910121415161820212224252627283032333435363839,2,2,2,5,2,2,3,2,
%U A241845 127,2,2,5,2,3,2,2,2,3,2,3,2,2
%N A241845 a(1)=1; for n >1 a(n) is the smallest prime divisor of the number obtained from concatenation of 1 and the first n-1 composites.
%C A241845 a(1)=1, and for n > 1 a(n) is the smallest prime divisor of the number obtained from the concatenation of A018252(j), j=1, ..., n. - _Wolfdieter Lang_, May 07 2014
%H A241845 Jinyuan Wang, <a href="/A241845/b241845.txt">Table of n, a(n) for n = 1..185</a>
%e A241845 1 U 4 = 14 and its divisors are 1, 2, 7, 14. Then a(2) = 2.
%e A241845 14 U 6 = 146 and its divisors are 1, 2, 73, 146. Then a(3) = 2.
%e A241845 146 U 8 = 1468 and its divisors are 1, 2, 4, 734, 367, 1468. Then a(4) = 2.
%e A241845 1468 U 9 = 14689 and its divisors are 1, 37, 397, 14689. Then a(5) = 37. Etc.
%p A241845 with(numtheory):
%p A241845 T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
%p A241845 P:=proc(q) local a,b,n; b:=1; print(1); for n from 2 to q do if not isprime(n) then b:=n+b*10^T(n); a:=sort([op(divisors(b))]); print(a[2]);
%p A241845 fi; od; end: P(10^6); # _Paolo P. Lava_, Apr 30 2014
%t A241845 Module[{nn=70,cmps},cmps=Select[Range[nn],CompositeQ];Join[ {1},SelectFirst[ Divisors[#],PrimeQ]&/@FromDigits/@Table[ Join[ {1},Flatten[ IntegerDigits/@Take[cmps,n]]],{n,Length[cmps]}]]] (* _Harvey P. Dale_, Jul 27 2021 *)
%Y A241845 Cf. A018252, A075019, A104644, A132934.
%K A241845 nonn,base
%O A241845 1,2
%A A241845 _Paolo P. Lava_, Apr 30 2014
%E A241845 More terms from _Jinyuan Wang_, Jun 27 2020