

A086204


Decimal equivalents of strings in A086884.


1



2, 2, 47, 151, 4001, 4001, 100207, 41532851, 447045215857, 282607273285049, 5678228814363947
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OFFSET

2,1


LINKS



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)


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR

Richard FitzHugh (fitzhughrichard(AT)hotmail.com), Aug 22 2003


EXTENSIONS



STATUS

approved



