A164328 a(n) is the smallest n-digit prime term of A158594 and zero if there is no such number.

7, 11, 271, 1033, 18289, 133733, 1045493, 11939237, 103333333, 1342313221, 10300335833, 145933933339, 1332523411733, 11653733331833

Offset: 1

Author

Farideh Firoozbakht, Sep 22 2009

Keywords

• base
• hard
• more
• nonn

Comments

It seems that for all n, a(n)>0.

A164327(n) gives us smallest n-digit term of A158594. So A164328(n)>=A164327(n).

Examples

			a(5)=18289 so all the seven numbers 18289, 318289, 138289, 183289, 182389,
182839 & 182893 are primes.
		

Crossrefs

Cf. A158594, A164327, A164329, A228148-A228150.

Programs

Mathematica

pp[n_, k_] := Catch[Block[{d = IntegerDigits@n}, Do[If[! PrimeQ[ FromDigits[ Insert[d, k, i]]], Throw[False]], {i, 1+Length@d}]; True]]; a[n_] := Catch[ Block[{p = NextPrime[10^(n-1)]}, While[p < 10^n, If[pp[p, 3], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[8] (* Giovanni Resta, Aug 13 2013 *)

Extensions

a(11)-a(13) from Donovan Johnson, Apr 14 2010

a(14) from Giovanni Resta, Aug 11 2013