A107342 Semiprimes with semiprime digits (digits 4, 6, 9 only).

4, 6, 9, 46, 49, 69, 94, 446, 466, 469, 649, 669, 694, 699, 949, 4449, 4469, 4499, 4666, 4694, 4699, 4946, 6499, 6646, 6649, 6694, 6999, 9446, 9449, 9466, 9469, 9946, 9969, 44494, 44669, 44949, 44966, 44969, 44999, 46469, 46666, 46946, 46969, 46994

Offset: 1

Author

Jonathan Vos Post, May 22 2005

Keywords

• base
• easy
• nonn

Comments

Numbers n such that all digits of n are elements of A001358 and n is an element of A001358.

Numbers n such that n is an element of A107665 and n is an element of A001358.

Conjecture: almost all terms (asymptotic density 1) end with 9 and have either 3k+1 or 3k+2 occurrences of the digit 4 for some nonnegative k. (Otherwise they'd be divisible by 2 or 3 and these semiprimes would be expected to be rare; the sequence is too thin to prove this directly.) - Charles R Greathouse IV, Nov 12 2021

Examples

			4 = 2^2
6 = 2 * 3
9 = 3^2
46 = 2 * 23
49 = 7^2
69 = 3 * 23
94 = 2 * 47
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..600

Crossrefs

Intersection of A001358 and A107665.

Cf. A029581, A107666, A111494, A111496, A111697, A254715.

Programs

Mathematica

fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2 && Union[ Join[{4, 6, 9}, IntegerDigits[n]]] == {4, 6, 9}; Select[ Range[ 47000], fQ[ # ] &] (* Robert G. Wilson v, May 27 2005 *)
Flatten[Table[Select[FromDigits/@Tuples[{4,6,9},n],PrimeOmega[#]==2&],{n,5}]] (* Harvey P. Dale, Jun 14 2015 *)

PARI

is(n)=bigomega(n)==2 && #setminus(Set(digits(n)),[4,6,9])==0 \\ Charles R Greathouse IV, Nov 12 2021

Extensions

More terms from Robert G. Wilson v, May 27 2005