A255579 Minimum prime p such that all the powers p^k, with k = 2, 3, …, n, are concatenations of two primes, while p^(k+1) is not.

5, 53, 17, 239, 773497, 37194173, 2208566719, 60669226939

Offset

2,1

Links

Table of n, a(n) for n=2..9.

Example

5^2 = 25 = concat(2,5); while 5^3 = 125 cannot be separated into two primes.
53^2 = 2809 = concat(2,809); 53^3 = 148877 = concat(14887,7); while 53^4 = 7890481 cannot be separated into two primes.
17^2 = 289 = concat(2,89); 17^3 = 4913 = concat(491,3); 17^4 = 83521 = concat(83,521); while 17^5 = 1419857 cannot be separated into two primes.

Maple

with(numtheory): T:=proc(x) local y, z; z:=0; for y from 1 to ilog10(x) do
if isprime(trunc(x/10^y)) and isprime(x mod 10^y) then z:=1; break; fi; od; z; end:
P:=proc(q) local a, k, n, ok; for a from 2 to q do
for n from 3 by 2 to q do if isprime(n) then ok:=1;
for k from 2 to a do if T(n^k)=0 then ok:=0; break; fi; od;
if ok=1 then if T(n^(a+1))=0 then print(n); break; fi; fi;
fi; od; od; end:  P(10^10);

Crossrefs

Cf. A000040, A255898.

Sequence in context: A215846 A216459 A107803 * A088712 A257667 A045711

Adjacent sequences: A255576 A255577 A255578 * A255580 A255581 A255582

Keyword

nonn,base,more,hard

Author

Paolo P. Lava, Oct 21 2015

Extensions

a(8)-a(9) from Giovanni Resta, May 31 2016

Status

approved