A117159 Prime numbers for which the multiplicative digital root is also a prime number.

2, 3, 5, 7, 13, 17, 31, 37, 43, 53, 71, 73, 113, 131, 137, 151, 157, 173, 211, 223, 311, 317, 359, 367, 389, 431, 557, 571, 593, 673, 751, 827, 839, 929, 953, 983, 1117, 1151, 1153, 1171, 1223, 1279, 1297, 1367, 1447, 1511, 1531, 1553, 1571, 1579, 1597, 1621

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 21 2006; corrected Apr 30 2006

Keywords

• base
• nonn

Examples

			157 is in the sequence because it is a prime number and its multiplicative digital root 5 is also a prime number.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000040 and A028843.

Cf. A031347.

Programs

Mathematica

a[n_]:=NestWhile[Times@@IntegerDigits[#]&,n,#>9&]; Select[Prime[Range[258]],PrimeQ[a[#]]&] (* Jayanta Basu, Jun 02 2013 *)