cp's OEIS Frontend

A294087 Least prime p_k such that (p_k)^n has p_{k+1} as substring.

%I A294087 #14 Feb 09 2018 11:37:49
%S A294087 23,11,37,2,7,5,3,41,3,13,3,3,2,2,2,2,5,5,5,3,2,2,3,2,3,2,2,2,2,2,3,2,
%T A294087 3,2,2,2,3,2,3,2,2,2,17,2,2,2,3,2,3,2,2,3,2,2,2,3,2,2,3,2,2,2,2,2,2,2,
%U A294087 2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2
%N A294087 Least prime p_k such that (p_k)^n has p_{k+1} as substring.
%C A294087 It appears that a(n) = 2 for n>153. In other words, for n>153, 3 is always a substring of 2^n. Is there any proof? See A035058.
%e A294087 23^2 = 529 and 29 is the prime after 23.
%e A294087 11^3 = 1331 and 13 is the prime after 11.
%e A294087 37^4 = 1874161 and 41 is the prime after 37.
%p A294087 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 A294087 if ok=1 then a:=ithprime(n); b:=nextprime(a); for k from 1 to ilog10(a^h)-ilog10(b)+1 do
%p A294087 if b=trunc(a^h/10^(k-1)) mod 10^(ilog10(b)+1) then print(a); ok:=0; break;
%p A294087 fi; od; fi; od; od; end: P(10^6);
%Y A294087 Cf. A035058, A052073, A052075, A294088.
%K A294087 nonn,easy,base
%O A294087 2,1
%A A294087 _Paolo P. Lava_, Feb 09 2018