A254928 - OEIS

%I #32 Dec 10 2016 19:37:07

%S 13,13,13,137,157163,153391501,153391501,1126903901803

%N Smallest (nontrivial) prime that, for each k from 2 to n, remains prime when each digit is replaced by the digit's k-th power.

%C Examples of trivial primes are 11, 101, etc, i.e., all primes in the sequence A020449: these generate themselves for all powers. These primes are excluded, otherwise all terms would be 11 since sequence wants smallest primes.

%e a(5) = 137; (1^k)&(3^k)&(7^k), where "&" represents concatenation of numbers:

%e for k=2, 1949 (prime), for k=3, 127343 (prime),

%e for k=4, 1812401 (prime), for k=5, 124316807 (prime).

%Y Cf. A020449 (primes that contain digits 0 and 1 only).

%Y Cf. A068492 (primes that remain prime after each digit is replaced by its square).

%Y Cf. A048393 (replacing digits d in decimal expansion of n with d^3 yields a prime).

%K nonn,base,hard,more

%O 2,1

%A _Abhiram R Devesh_, May 04 2015

%E a(9) from _Giovanni Resta_, May 19 2015