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Smallest of four consecutive primes whose product of digits is equal and nonzero.
0

%I #8 Jan 27 2015 13:37:06

%S 336737123,812444239,1731191219,2187575239,2549315123,2672459219,

%T 2721498343,2778476123,2781452239,2924114819,2925926819,3232115219,

%U 3441686219,3579455219,3617846123,3755345219,3943951637

%N Smallest of four consecutive primes whose product of digits is equal and nonzero.

%e 336737123 is in the sequence because 336737123, 336737161, 336737213 and 336737231 are consecutive primes and the product of the digits of each = 47628.

%t a = {}; m = 1; s = 1; Do[If[(y = Apply[Times, IntegerDigits[x = Prime[n]]]) == s && s != 0, m = m + 1; If[m > 3, AppendTo[a, Prime[n - 3]]], m = 1]; s = y, {n, 1, 200000000}]; a

%t pdeQ[{a_,b_,c_,d_}]:=Module[{u=Union[Times@@@(IntegerDigits/@{a,b,c,d})]}, Length[ u] ==1&&u[[1]]>0]; Transpose[Select[Partition[Prime[Range[ 19*10^7]],4,1],pdeQ]][[1]] (* _Harvey P. Dale_, Jan 27 2015 *)

%Y Cf. A230082, A230083, A230084, A007954, A053666.

%K nonn,base

%O 1,1

%A _Shyam Sunder Gupta_, Oct 08 2013