OFFSET
2,1
LINKS
Mersenneforum.org, Multibase primes
EXAMPLE
a(5) = 10010111 because 10010111 (base 2) = 151, 10010111 (base 3) = 2281, 10010111 (base 4) = 16661 and 10010111 (base 5) = 78781 are all prime and 10010111 is the smallest such string.
MATHEMATICA
a[n_] := (While[b = FromDigits[ IntegerDigits[k, 2]]; Union[ PrimeQ[ Table[ FromDigits[ IntegerDigits[b], i], {i, 2, n}]]] != {True}, k++ ]; b); k = 1; Do[ Print[ a[n]], {n, 2, 10}]
PROG
(Python)
from sympy import isprime
def conv(s, b): return sum(b**k for k, bk in enumerate(s[::-1]) if bk=='1')
def ok(s, n): return all(isprime(conv(s, b)) for b in range(2, n+1))
def a(n):
if n < 4: return 2
k = 3
while not ok(bin(k)[2:], n): k += 2
return int(bin(k)[2:], 2)
print([a(n) for n in range(2, 9)]) # Michael S. Branicky, Oct 10 2021
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Richard FitzHugh (fitzhughrichard(AT)hotmail.com), Aug 22 2003
EXTENSIONS
Edited by Robert G. Wilson v, Aug 24 2003
Two more terms added by James G. Merickel, Feb 15 2010
One more term added by Andreas Höglund, Oct 17 2022 (found by Jim Viebke)
STATUS
approved