A228149 -id:A228149 - cp's OEIS frontend

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

Giovanni Resta, Aug 13 2013

Smallest n-digit term of A069246.

			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.

Cf. A069246, A164328, A228149, A228150.

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]

A228150 a(n) is the smallest n-digit prime which remains prime whenever a 9 is inserted, appended or prepended, or 0 if no such prime exists.

Original entry on oeis.org

7, 19, 199, 1009, 19417, 160009, 1086791, 10301299, 139993999, 1391909989, 10597399381, 108979916999, 1993999651909, 13924969999799

Offset: 1

Giovanni Resta, Aug 13 2013

Smallest n-digit term of A215421.

			a(4) = 1009 is the smallest 4-digit prime which yields 5 primes by inserting a 9 in every possible position: 91009, 19009, 10909, 10099, 10099.

Cf. A215421, A164328, A228148, A228149.

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, 9], Throw@p, p = NextPrime@p]]; 0]]; a /@ Range[8]

cp's OEIS Frontend

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.

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