%I
%S 23,30,32,33,34,38,63,83,103,130,131,132,143,153,235,238,311,314,330,
%T 333,338,341,343,344,345,346,349,353,354,355,356,357,360,361,366,368,
%U 370,371,378,396,399,432,433,434,435,438,439,443,453,463,473,513,523
%N Numbers n such that n and nth prime have only one common digit = 3.
%C Other cases of common digit d: A107931 (d=0), A107932 (d=1), A107933 (d=2), A107935 (d=4), A107936 (d=5), A107937 (d=6), A107938 (d=7), A107939 (d=8), A107940 (d=9). Cf. A107930  smallest m's for digits 0,...,9.
%H Robert Israel, <a href="/A107934/b107934.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=23 because 23rd prime, 83 and 23 have 3 as their only common digit, and 23 is the smallest such number.
%p filter:= n > convert(convert(n,base,10),set) intersect convert(convert(ithprime(n),base,10),set) = {3}:
%p select(filter, [$1..1000]); # _Robert Israel_, May 10 2021
%t bb={};Do[If[IntegerDigits [n]\[Intersection]IntegerDigits [ Prime[n]]\[Equal]{3}, bb=Append[bb, n]], {n, 1800}];bb
%Y Cf. A107930  A107940.
%K nonn,base
%O 1,1
%A _Zak Seidov_, May 28 2005
