A360494 a(n) is the least number that is prime when interpreted in bases 2 to n, but not n+1.

11, 10, 101111, 10010111, 110111111101001, 111110100001, 11000011101101111, 10011110011011110110110011, 110100000010101111110001010011001110001, 1000000010000011110100010001000101001010110111001, 10100001011000101000110101011011011101111110100101011

Offset

2,1

Comments

Since a(n) must be a valid base-2 integer, it can only have digits 0 and 1.

Links

Table of n, a(n) for n=2..12.

Example

a(4) = 101111 because 101111 interpreted in base-2 is 47 (prime), base-3 is 283 (prime), base-4 is 1109 (prime), but base-5 is 3281 (not prime).

Maple

V:= Vector(9): count:= 0:
f:= proc(n) local L, P, x, b, i;
      L:= convert(n, base, 10);
      P:= add(L[i]*x^(i-1), i=1..nops(L));
      for b from 2 do if not isprime(eval(P, x=b)) then return b-1 fi od
end proc:
for i from 1 while count < 8 do
  X:= convert(i, binary);
  v:= f(X);
  if v >= 1 and v <= 9 and V[v] = 0 then
    V[v]:= X;
    count:= count+1;
  fi
od:
convert(V[2..9], list);

Prog

(Python)
from sympy import isprime
from itertools import count, islice, product
def f(s): return next(b-1 for b in count(2) if not isprime(int(s, b)))
def agen():
    n, adict = 2, {2:11, 3:10}
    for d in count(3):
        for b in product("01", repeat=d-2):
            s = "1" + "".join(b) + "1"
            v = f(s)
            if v not in adict: adict[v] = int(s)
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 7))) # Michael S. Branicky, Feb 09 2023

Crossrefs

Cf. A086884.

Sequence in context: A164125 A212529 A004289 * A287710 A287782 A167262

Adjacent sequences: A360491 A360492 A360493 * A360495 A360496 A360497

Keyword

nonn,base

Author

Robert Israel, Feb 09 2023

Extensions

a(10)-a(12) using A086884 from Michael S. Branicky, Feb 09 2023

Status

approved