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 A107934 Numbers n such that n and n-th prime have only one common digit = 3. 4

%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 n-th 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

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Last modified August 10 07:57 EDT 2022. Contains 356036 sequences. (Running on oeis4.)