OFFSET
2,1
COMMENTS
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.
EXAMPLE
23^2 = 529 and 29 is the prime after 23.
11^3 = 1331 and 13 is the prime after 11.
37^4 = 1874161 and 41 is the prime after 37.
MAPLE
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
if ok=1 then a:=ithprime(n); b:=nextprime(a); for k from 1 to ilog10(a^h)-ilog10(b)+1 do
if b=trunc(a^h/10^(k-1)) mod 10^(ilog10(b)+1) then print(a); ok:=0; break;
fi; od; fi; od; od; end: P(10^6);
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, Feb 09 2018
STATUS
approved