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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.
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%I #12 Jun 13 2021 03:29:33

%S 3,13,103,1117,11119,114031,1114693,11213611,101116111,1013251111,

%T 10116171733,101346411811,1011670114111,11111117116117

%N 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.

%C Smallest n-digit term of A069246.

%e 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.

%t 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]

%Y Cf. A069246, A164328, A228149, A228150.

%K nonn,base,more

%O 1,1

%A _Giovanni Resta_, Aug 13 2013