A255898 Minimum prime p such that p^n is a concatenation of two primes.

23, 5, 3, 7, 2, 3, 43, 47, 3, 3, 7, 11, 17, 11, 3, 29, 3, 11, 3, 109, 11, 43, 71, 19, 71, 11, 11, 3, 7, 229, 43, 269, 7, 23, 3, 61, 37, 677, 113, 863, 59, 3, 11, 487, 359, 347, 3, 19, 53, 173, 3, 127, 229, 7, 3, 3, 13, 3, 241, 41, 79, 79, 3, 83, 23, 31, 71, 31

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Example

23^1 = 23 = concat(2,3);
5^2 = 25 = concat(2,5);
3^3 = 27 = concat(2,7).

Maple

with(numtheory): P:= proc(q) local a, k, n, ok;
for a from 1 to q do for n from 1 to q do if isprime(n) then ok:=0;
for k from 1 to ilog10(n^a) do if isprime(trunc(n^a/10^k)) and isprime(n^a mod 10^k) then ok:=1; break; fi; od;
if ok=1 then lprint(a, n); break; fi; fi; od; od; end: P(10^9);

Mathematica

mp[n_]:=Module[{p=2}, While[Count[PrimeQ[#]&/@Table[FromDigits/@ TakeDrop[ IntegerDigits[ p^n], i], {i, IntegerLength[p^n]}], {True, True}]== 0, p= NextPrime[ p]]; p]; Array[mp, 70] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 13 2016 *)

Prog

(PARI) a(n) = {forprime(p=2, , my(pn = p^n); for (k=1, #Str(pn), if (isprime(pn\10^k) && isprime(pn % 10^k), return (p)); ); ); } \\ Michel Marcus, Oct 22 2015

Crossrefs

Cf. A000040, A255579.

Sequence in context: A040515 A040516 A040513 * A281923 A040514 A098103

Adjacent sequences: A255895 A255896 A255897 * A255899 A255900 A255901

Keyword

nonn,base,easy

Author

Paolo P. Lava, Oct 21 2015

Status

approved