A230084 Smallest of three consecutive primes whose product of digits is equal and nonzero.

442619, 2483219, 6325619, 7567919, 7886519, 9883673, 9962219, 11117123, 14669519, 15446819, 17958419, 21337279, 23623129, 26453671, 26872919, 27234419, 27536519, 27948343, 32638213, 32964341, 33539783, 33813419, 34277819, 34554719, 35732381, 37571519

Offset: 1

Author

Shyam Sunder Gupta, Oct 08 2013

Keywords

• nonn
• base

Examples

			442619 is in the sequence because 442619,442633 and 442691 are consecutive primes and the product of the digits of each = 1728.
		

Links

• Shyam Sunder Gupta, Table of n, a(n) for n = 1..1713

Crossrefs

Cf. A230082, A230083, A007954, A053666.

Programs

Mathematica

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
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 *)
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 *)