A064156 Smallest prime with n decimal digits such that the product of its digits equals n times the sum of its digits, or 0 if no such prime exists.

2, 0, 167, 1427, 0, 126241, 1111457, 12222241, 111113543, 0, 0, 111111118273, 0, 0, 111111111126581, 1111111111144841, 0, 111111111111126443, 0, 11111111111122225421, 111111111111111135781, 0, 0, 111111111111111111244561, 1111111111111111121255521, 0, 111111111111111111111113797

Offset: 1

Author

Felice Russo, Sep 14 2001

Keywords

• nonn
• base

Examples

			167 belongs to the sequence because this is the smallest prime with 3 digits such that 1*6*7=42 and 3*(1+6+7)=42
		

Links

• Max Alekseyev, Table of n, a(n) for n=1..200

Programs

Mathematica

NextPrim[ n_ ] := (k = n + 1; While[ ! PrimeQ[ k ], k++ ]; k); Do[ If[ n != 1 && Transpose[ FactorInteger[ n ] ][ [ 1, -1 ] ] <= 10, k = NextPrim[ (10^n - 1)/9 ];
While[ d = IntegerDigits[ k ]; k < 10^n && n*Apply[ Plus, d ] != Apply[ Times, d ], k = NextPrim[ k ] ]; If[ k < 10^n, Print[ k ], Print[ 0 ] ], If[ n == 1, Print[ 2 ], Print[ 0 ] ] ], {n, 1, 9} ]

Extensions

Corrected and extended by Robert G. Wilson v, Oct 05 2001

a(14), a(20), a(25) and b-file from Max Alekseyev, May 07 2009