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%I #9 Feb 01 2022 14:56:48
%S 442619,2483219,6325619,7567919,7886519,9883673,9962219,11117123,
%T 14669519,15446819,17958419,21337279,23623129,26453671,26872919,
%U 27234419,27536519,27948343,32638213,32964341,33539783,33813419,34277819,34554719,35732381,37571519
%N Smallest of three consecutive primes whose product of digits is equal and nonzero.
%H Shyam Sunder Gupta, <a href="/A230084/b230084.txt">Table of n, a(n) for n = 1..1713</a>
%e 442619 is in the sequence because 442619,442633 and 442691 are consecutive primes and the product of the digits of each = 1728.
%t a = {}; m = 1; s = 1; Do[ If[(y = Apply[Times, IntegerDigits[x = Prime[n]]]) == s && s != 0, m = m + 1; If[m > 2, AppendTo[a, Prime[n - 2]]], m = 1]; s = y, {n, 1, 100000}]; a
%t Transpose[Select[Partition[Prime[Range[23*10^5]],3,1],Times@@ IntegerDigits[ #[[1]]]==Times@@IntegerDigits[#[[2]]] == Times@@ IntegerDigits[#[[3]]]>0&]][[1]] (* _Harvey P. Dale_, Apr 05 2016 *)
%t pdeQ[{a_,b_,c_}]:=Module[{un=Union[Times@@@IntegerDigits[{a,b,c}]]},un != {0} && Length[un]==1]; Select[Partition[Prime[Range[23*10^5]],3,1],pdeQ][[All,1]] (* _Harvey P. Dale_, Feb 01 2022 *)
%Y Cf. A230082, A230083, A007954, A053666.
%K nonn,base
%O 1,1
%A _Shyam Sunder Gupta_, Oct 08 2013
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