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A360494
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a(n) is the least number that is prime when interpreted in bases 2 to n, but not n+1.
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0
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11, 10, 101111, 10010111, 110111111101001, 111110100001, 11000011101101111, 10011110011011110110110011, 110100000010101111110001010011001110001, 1000000010000011110100010001000101001010110111001, 10100001011000101000110101011011011101111110100101011
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OFFSET
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2,1
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COMMENTS
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Since a(n) must be a valid base-2 integer, it can only have digits 0 and 1.
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LINKS
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EXAMPLE
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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).
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MAPLE
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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);
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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