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Smallest prime starting with 1 that contains exactly n 0's.
2

%I #13 Aug 30 2020 13:50:07

%S 101,1009,10007,100003,1000003,100000037,100000007,1000000007,

%T 100000000019,100000000003,10000000000037,100000000000031,

%U 1000000000000037,10000000000000061,100000000000000013

%N Smallest prime starting with 1 that contains exactly n 0's.

%H Harvey P. Dale, <a href="/A139535/b139535.txt">Table of n, a(n) for n = 1..100</a>

%t sp0[n_]:=Module[{c=1,d},While[d=FromDigits[Join[PadRight[{1},n+1,0],IntegerDigits[ c]]];DigitCount[d,10,0]>n||CompositeQ[d],c=c+2];FromDigits[ Join[ PadRight[ {1},n+1,0],IntegerDigits[c]]]]; Array[sp0,20] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 30 2020 *)

%Y Cf. A037053, A003617, A139536.

%K nonn,base

%O 1,1

%A _Lekraj Beedassy_, Apr 25 2008