A368337 Semiprimes that contain only digits 4 and 9.

4, 9, 49, 94, 949, 4449, 4499, 9449, 44494, 44949, 44999, 49949, 94499, 94994, 99449, 99494, 99949, 444494, 444949, 494449, 494999, 499949, 944494, 944949, 944999, 949999, 994999, 999494, 4444449, 4444499, 4449949, 4449999, 4494449, 4494499, 4494949, 4494999, 4499449, 4499494, 4944449, 4944499

Offset: 1

Author

Zak Seidov and Robert Israel, Dec 21 2023

Keywords

• nonn
• base

Comments

The only terms that are squares are 4, 9 and 49.

Numbers of n-digit terms for n = 1...20: {2, 2, 1, 3, 13, 11, 31, 39, 78, 159, 383, 541, 1302, 2047, 4268, 6926, 16248, 27172, 57397, 94581}.

Examples

			a(3) = 49 is a term because 49 = 7^2 is a semiprime with digits 4 and 9.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A001358 and A284973.

Cf. A020466.

Programs

Maple

R:= 4,9:
for d from 2 to 6 do
  for x from 0 to 2^d-1 do
    L:= convert(2^d+x,base,2)[1..d];
    y:= add((L[i]*5+4)*10^(i-1),i=1..d);
    if numtheory:-bigomega(y)=2 then R:= R,y; fi
od od:
R;