A254928 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.

13, 13, 13, 137, 157163, 153391501, 153391501, 1126903901803

Offset: 2

Author

Abhiram R Devesh, May 04 2015

Keywords

• nonn
• base
• hard
• more

Comments

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.

Examples

			a(5) = 137; (1^k)&(3^k)&(7^k), where "&" represents concatenation of numbers:
for k=2, 1949 (prime), for k=3, 127343 (prime),
for k=4, 1812401 (prime), for k=5, 124316807 (prime).
		

Crossrefs

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

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

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

Extensions

a(9) from Giovanni Resta, May 19 2015