OFFSET

2,1

COMMENTS

a(n), n > 6, is intractable, and a(6) requires extensive resources: There are 360 candidate numbers for any candidate prime, all of which need to be composite, prefixing 30 2-digit numbers and suffixing the 12 ending in either 1 or 5. This compares with 400 for base 5, but in the base-6 case divisibility by 2 and 3 are already ruled out.

EXAMPLE

In base 2--binary, decimal 2 and 3 have representations 10 and 11; and binary 101001 and 101111 represent decimal 41 and 47, so that a(2) > 3. Binary 101--decimal 5--has the 4 binary candidates 1010101, 1010111, 1110101, and 1110111--decimal 85, 87, 117 and 119--requiring consideration for primality, but all are composite: a(2)=5.

PROG

(PARI) ok(n, b)=my(D=b^#digits(n, b), b2=b^2); forstep(k=b^3*D+n*b2, b2*(b2-1)*D+n*b2, D*b2, if(nextprime(k)<k+b2, return(0))); 1

a(n)=forprime(p=2, , if(ok(p, n), return(p))) \\ Charles R Greathouse IV, Sep 20 2014

CROSSREFS

KEYWORD

nonn,base,more,hard

AUTHOR

James G. Merickel, Sep 20 2014

STATUS

approved