A374897 a(n) is the least semiprime that ends with n, or -1 if there is no such semiprime.

10, 21, 22, 33, 4, 15, 6, 57, 38, 9, 10, 111, -1, 213, 14, 15, -1, 217, 118, 119, -1, 21, 22, 123, -1, 25, 26, 327, -1, 129, -1, 731, -1, 33, 34, 35, -1, 237, 38, 39, -1, 141, 142, 143, -1, 145, 46, 247, -1, 49, -1, 51, -1, 253, 254, 55, -1, 57, 58, 159, -1, 161, 62, 763, -1, 65, 166, 267, -1, 69

Offset: 0

Author

Zak Seidov and Robert Israel, Jul 22 2024

Keywords

• sign
• base
• look

Comments

a(n) = -1 if n > 10 and n is divisible by 4 or 10, or n > 25 and n is divisible by 25. Otherwise a(n) > 0 (which can be proven using Dirichlet's theorem on primes in arithmetic progressions).

Examples

			a(5) = 15 because 15 = 3*5 is a semiprime and ends in 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001358, A070277, A374899.

Programs

Maple

f:= proc(n) local x,d;
  if (n mod 4 = 0 and n > 10) or (n mod 10 = 0) or (n mod 25 = 0) then return -1 fi;
  d:= 10^(1+ilog10(n));
  for x from n by d do
    if numtheory:-bigomega(x) = 2 then return x fi
  od
end proc:
f(0):= 10:
f(10):= 10:
f(25):= 25:
map(f, [$1..100]);