

A221700


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


0



5, 409, 409, 409, 9721, 47881, 47881, 47881, 10366201, 84768121, 35581939201, 45711198721, 5878291093921, 5878291093921, 5878291093921
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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++]; b1]; 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: A221047 A075769 A046274 * A216089 A201887 A301309
Adjacent sequences: A221697 A221698 A221699 * A221701 A221702 A221703


KEYWORD

nonn,base,hard


AUTHOR

Giovanni Resta, Feb 22 2013


STATUS

approved



