A221700 a(n) is the smallest prime p > n which cannot become prime by removing any number of initial digits in bases 2,...,n.

5, 409, 409, 409, 9721, 47881, 47881, 47881, 10366201, 84768121, 35581939201, 45711198721, 5878291093921, 5878291093921, 5878291093921

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..16.

Example

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.

Mathematica

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]]

Crossrefs

Cf. A196095, A211972.

Sequence in context: A368021 A075769 A046274 * A216089 A201887 A365370

Adjacent sequences: A221697 A221698 A221699 * A221701 A221702 A221703

Keyword

nonn,base,hard

Author

Giovanni Resta, Feb 22 2013

Status

approved