A108636 Semiprimes with even digits.

4, 6, 22, 26, 46, 62, 82, 86, 202, 206, 226, 262, 422, 446, 466, 482, 622, 626, 662, 802, 842, 862, 866, 886, 2026, 2042, 2062, 2066, 2206, 2246, 2402, 2426, 2446, 2462, 2602, 2606, 2642, 2846, 2866, 4006, 4022, 4222, 4226, 4262, 4282, 4286, 4406, 4426, 4442

Offset: 1

Author

Zak Seidov, Jun 14 2005

Keywords

• nonn
• base
• look

Comments

Semiprimes with even digits are less numerous than those with odd digits, cf. A091296.

"Semiprimes with even digits are less numerous than those with odd digits" because (base 10): no integer after 10 can end in a 0 without being divisible by 2, 5 and at least one other prime; for a semiprime to end in 2, 4, 6, or 8 it must be divisible by 2 and a prime with almost as many digits as the semiprime (and primes get rarer as they get longer); no semiprime with all even digits after 22 can be a repdigit; and similar constraints. - Jonathan Vos Post, Nov 07 2005

Links

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

Crossrefs

Intersection of A001358 and A014263.

Cf. A091296.

Programs

Maple

f:= proc(n) local L,x,i;
  L:= convert(n,base,5);
  x:= 2*add(L[i]*10^(i-1),i=1..nops(L));
  if isprime(x/2) then x else NULL fi
end proc:
map(f, [$1..1000]); # Robert Israel, Oct 01 2024

Mathematica

Select[Range[6000], Plus@@Last/@FactorInteger[ # ]==2&&Union[EvenQ/@IntegerDigits[ # ]]=={True}&]