A221700 - OEIS

%I #16 Feb 22 2013 17:18:17

%S 5,409,409,409,9721,47881,47881,47881,10366201,84768121,35581939201,

%T 45711198721,5878291093921,5878291093921,5878291093921

%N a(n) is the smallest prime p > n which cannot become prime by removing any number of initial digits in bases 2,...,n.

%C The condition a(n) > n is introduced because 2 and 3 trivially satisfy the condition in every base b >= 2.

%e 409 = (110011001)_2 = (120011)_3 and none of the numbers (10011001)_2, (11001)_2, (1001)_2, (1)_2, (20011)_3, (11)_3, (1)_3 is prime. Since 409 is the smallest prime p > 3 with this property, a(3) = 409.

%t mx[n_] := Block[{b = 2}, While[Not[Or @@ PrimeQ@Mod[n, b^Range@Floor@ Log[b, n]]], b++]; b-1]; c=1; n=5; While[n < 15^6, If[mx[n] > c, Print@{++c, n}, n = NextPrime@n]]

%Y Cf. A196095, A211972.

%K nonn,base,hard

%O 2,1

%A _Giovanni Resta_, Feb 22 2013