A228149 a(n) is the smallest n-digit prime which remains prime whenever a 7 is inserted, appended or prepended, or 0 if no such prime exists.

3, 19, 433, 1471, 13177, 175687, 1740787, 10871017, 137725897, 1670181787, 12845952529, 117777772309, 1008078796477, 11777787780727

Offset: 1

Author

Giovanni Resta, Aug 13 2013

Keywords

• nonn
• base
• more

Comments

Smallest n-digit term of A215420.

Examples

			a(3) = 433 is the smallest 3-digit prime which yields 4 primes by inserting a 7 in every possible position: 7433, 4733, 4373, 4337.
		

Crossrefs

Cf. A215420, A164328, 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, 7], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[8]