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

1,1

Links

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

Example

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

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} ]

Crossrefs

Sequence in context: A003321 A012333 A012329 * A269905 A012335 A012331

Adjacent sequences: A064153 A064154 A064155 * A064157 A064158 A064159

Keyword

nonn,base

Author

Felice Russo, Sep 14 2001

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

Status

approved