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%I #25 Dec 08 2021 16:02:25
%S 0,131,1416641,151,16361,17491,181,191,0,1111211,
%T 11214417282073624883229859841,0,11419627441,1151,
%U 1162564096655361048576167772162684354564294967296687194767361099511627776175921860444161,1171,1181,11936168591,1201
%N The smallest prime number formed by the concatenation of consecutive powers of n beginning with 1^0 = "1," and ending with a trailing "1" - or "0," if no such prime number exists.
%C It is not known whether solutions exist for A(2), A(10), or A(13); if there are any, they must be greater than 10^128.
%C A(10) has final exponent 35; "110100100010000...1000000000000000000000000000000000001", total length 667 digits. - _Dana Jacobsen_, Jan 22 2016
%C A(2) has exponent > 1100, length > 182841 digits. A(13) has exponent > 750, length > 314093 digits. - _Dana Jacobsen_, Jan 25 2016
%e A(14)=11419627441; 14^0=1; 14^1=14; 14^2=196; 14^3=2744; 11419627441 is prime.
%e A(19)=11936168591; 19^0=1; 19^1=19; 19^2=361; 19^3=6859; 11936168591 is prime.
%t lim = 60; Table[SelectFirst[Rest@ FoldList[FromDigits@ Join[Most@ IntegerDigits@ #1, IntegerDigits[n^#2], {1}] &, 11, Range@ lim], PrimeQ], {n, 2, 20}] /. k_ /; MissingQ@ k -> 0 (* _Michael De Vlieger_, Jan 25 2016, Version 10.2 *)
%Y Cf. A068704, A088622.
%K nonn,base
%O 2,2
%A _Thomas S. Pedigo_, Jan 19 2016
%E a(8) corrected by _Thomas S. Pedigo_, Dec 08 2021