A118690 Semiprimes for which both the sum and the product of the digits is also a semiprime.

4, 6, 9, 22, 33, 55, 77, 91, 123, 141, 177, 213, 217, 321, 411, 717, 721, 771, 1135, 1157, 1315, 1351, 1513, 1517, 1751, 3151, 5131, 5311, 7115, 11157, 11215, 11521, 11611, 11751, 12115, 12151, 15117, 15711, 17151, 21151, 51211, 57111, 61111, 75111

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..128

Example

91 is in the sequence because (1) it is a semiprime, (2) the sum of its digits is 9+1=10, (3) the product of its digits is 1*9=9 and (4) both 9 and 10 are semiprimes.

Mathematica

spQ[n_] := Plus @@ Last /@ FactorInteger@n == 2; fQ[n_] := Block[{id = IntegerDigits@n}, spQ@n && spQ[Plus @@ id] && spQ[Times @@ id]]; Select[ Range@111172, fQ@# &] (* Robert G. Wilson v, Jun 15 2006 *)
Select[Range[76000], Thread[PrimeOmega[{#, Total[IntegerDigits[#]], Times@@ IntegerDigits[#]}]] == {2, 2, 2}&]  (* Harvey P. Dale, Jul 26 2022 *)

Crossrefs

Cf. A001358.

Sequence in context: A137253 A035135 A046338 * A084994 A046328 A196104

Adjacent sequences: A118687 A118688 A118689 * A118691 A118692 A118693

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 20 2006

Extensions

More terms from Robert G. Wilson v, Jun 15 2006

Status

approved