A388300 - OEIS

%I #13 Sep 29 2025 18:57:22

%S 2,11,11,101,11,13,13,13,101,23,13,31,13,23,31,101,17,103,19,41,211,

%T 10111,19,41,101,43,103,131,19,43,19,113,1021,43,19,211,53,103,37,131,

%U 19,223,19,113,1201,101111,53,61,101,47,103,311,19,313,211,71,2011,113,19,331,19,223,71,101,73

%N a(n) is the base-A388299(n) representation of n.

%C a(n) is the base-b representation of n for the smallest base b>=2 such that this base-b representation is the base-10 representation of a prime.

%H Robert Israel, <a href="/A388300/b388300.txt">Table of n, a(n) for n = 2..10000</a>

%e a(5) = 101 because 5 = 101_2 and 101 is prime.

%p f:= proc(n) local b,L,i,p;

%p   for b from 2 do

%p     L:= convert(n,base,b);

%p     if max(L) > 9 then next fi;

%p     p:= add(L[i]*10^(i-1),i=1..nops(L));

%p     if isprime(p) then return p fi

%p   od

%p end proc:

%p map(f, [$2..100]);

%t a[n_]:=Module[{b=2}, While[!ContainsOnly[IntegerDigits[n, b], Range[0, 9]]||!PrimeQ[FromDigits[IntegerDigits[n, b]]], b++]; FromDigits[IntegerDigits[n,b]]]; Array[a, 65, 2]  (* _James C. McMahon_, Sep 25 2025 *)

%Y Cf. A388299.

%K nonn,base,look

%O 2,1

%A _Robert Israel_, Sep 16 2025