A107342 - OEIS

%I #19 Nov 12 2021 21:00:21

%S 4,6,9,46,49,69,94,446,466,469,649,669,694,699,949,4449,4469,4499,

%T 4666,4694,4699,4946,6499,6646,6649,6694,6999,9446,9449,9466,9469,

%U 9946,9969,44494,44669,44949,44966,44969,44999,46469,46666,46946,46969,46994

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

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

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

%C 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

%H Vincenzo Librandi, <a href="/A107342/b107342.txt">Table of n, a(n) for n = 1..600</a>

%e 4 = 2^2

%e 6 = 2 * 3

%e 9 = 3^2

%e 46 = 2 * 23

%e 49 = 7^2

%e 69 = 3 * 23

%e 94 = 2 * 47

%t 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 *)

%t Flatten[Table[Select[FromDigits/@Tuples[{4,6,9},n],PrimeOmega[#]==2&],{n,5}]] (* _Harvey P. Dale_, Jun 14 2015 *)

%o (PARI) is(n)=bigomega(n)==2 && #setminus(Set(digits(n)),[4,6,9])==0 \\ _Charles R Greathouse IV_, Nov 12 2021

%Y Intersection of A001358 and A107665.

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

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, May 22 2005

%E More terms from _Robert G. Wilson v_, May 27 2005