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Composite numbers with both additive and multiplicative digital roots prime.
2

%I #19 Jun 03 2013 13:54:32

%S 12,21,34,57,75,115,232,299,322,371,376,398,511,579,597,637,713,731,

%T 736,759,763,795,893,938,957,975,992,1112,1121,1137,1157,1173,1175,

%U 1211,1299,1317,1355,1371,1389,1398,1469,1474,1496,1517,1535,1649,1694

%N Composite numbers with both additive and multiplicative digital roots prime.

%e 322 is here since for 322 additive digital root is 7 and multiplicative digital root is 2, both are primes.

%t a[n_] := NestWhile[Times@@IntegerDigits[#]&, n, #>9&]; Select[Range[1700], !PrimeQ[#] && And@@PrimeQ[{a[#], Mod[#,9]}]&]

%Y Cf. A028835, A028843.

%K nonn,base

%O 1,1

%A _Jayanta Basu_, Jun 03 2013