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%I #15 Feb 09 2018 11:38:48
%S 3701,3,43,3,3,3,5,5,7,11,11,3,3,5,3,3,3,3,5,3,5,3,3,3,3,3,3,5,3,3,3,
%T 3,5,5,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,3,3,3,3,5,3,3,3,3,3,3,3,
%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N Least prime p_k such that (p_k)^n has p_{k-1} as substring.
%C It appears that a(n) = 3 for n>59. In other words, for n>59, 2 is always a substring of 3^n. Is there any proof? See A131625.
%e 3701^2 = 13697401 and 3697 is the prime before 3701.
%e 3^3 = 27 and 2 is the prime before 3.
%e 43^4 = 3418801 and 41 is the prime before 43.
%p P:=proc(q) local a,b,h,k,n,ok; for h from 2 to q do ok:=1; for n from 1 to q do
%p if ok=1 then a:=ithprime(n); b:=prevprime(a); for k from 1 to ilog10(a^h)-ilog10(b)+1 do
%p if b=trunc(a^h/10^(k-1)) mod 10^(ilog10(b)+1) then print(a); ok:=0; break;
%p fi; od; fi; od; od; end: P(10^6);
%Y Cf. A052073, A052075, A131625, A294087.
%K nonn,easy,base
%O 2,1
%A _Paolo P. Lava_, Feb 09 2018
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