A228148 a(n) is the smallest n-digit prime which remains prime whenever a 1 is inserted, appended or prepended, or 0 if no such prime exists.

3, 13, 103, 1117, 11119, 114031, 1114693, 11213611, 101116111, 1013251111, 10116171733, 101346411811, 1011670114111, 11111117116117

Offset: 1

Author

Giovanni Resta, Aug 13 2013

Keywords

• nonn
• base
• more

Comments

Smallest n-digit term of A069246.

Examples

			a(3) = 103 is the smallest 3-digit prime which yields 4 primes by inserting a 1 in every possible position: 1103, 1103, 1013, 1031.
		

Crossrefs

Cf. A069246, A164328, A228149, 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, 1], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[7]