A388300 a(n) is the base-A388299(n) representation of n.

2, 11, 11, 101, 11, 13, 13, 13, 101, 23, 13, 31, 13, 23, 31, 101, 17, 103, 19, 41, 211, 10111, 19, 41, 101, 43, 103, 131, 19, 43, 19, 113, 1021, 43, 19, 211, 53, 103, 37, 131, 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

Offset

2,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Example

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

Maple

f:= proc(n) local b, L, i, p;
  for b from 2 do
    L:= convert(n, base, b);
    if max(L) > 9 then next fi;
    p:= add(L[i]*10^(i-1), i=1..nops(L));
    if isprime(p) then return p fi
  od
end proc:
map(f, [$2..100]);

Mathematica

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 *)

Crossrefs

Cf. A388299.

Sequence in context: A290394 A292779 A245521 * A275617 A090009 A153706

Adjacent sequences: A388297 A388298 A388299 * A388301 A388302 A388303

Keyword

nonn,base,look

Author

Robert Israel, Sep 16 2025

Status

approved