OFFSET
1,1
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}.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 49 is a term because 49 = 7^2 is a semiprime with digits 4 and 9.
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;
MATHEMATICA
Select[Flatten[Table[FromDigits/@Tuples[{4, 9}, n], {n, 7}]], PrimeOmega[#]==2&] (* Harvey P. Dale, Jan 08 2026 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Zak Seidov and Robert Israel, Dec 21 2023
STATUS
approved