A254923 The slowest increasing sequence of semiprimes with alternating parity.

4, 9, 10, 15, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 58, 65, 74, 77, 82, 85, 86, 87, 94, 95, 106, 111, 118, 119, 122, 123, 134, 141, 142, 143, 146, 155, 158, 159, 166, 169, 178, 183, 194, 201, 202, 203, 206, 209, 214, 215, 218, 219, 226, 235, 254, 259, 262, 265, 274, 287, 298, 299, 302, 303, 314

Offset

1,1

Comments

a(n) is the least semiprime > a(n-1) such that (a(n) mod 2) != (a(n-1) mod 2).

Links

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

Example

The sequence starts with 4, which is even.
The next semiprime is 6, but that's also even, so 6 is skipped over and the sequence continues with 9, which is odd.
The next semiprime is 10, and since that's even, it's the next term in the sequence.

Maple

R:= 4: x:= 3: count:= 1:
while count < 100 do
  x:= x+2;
  if numtheory:-bigomega(x) = 2 then
    count:= count+1; R:= R, x; x:= x-1
  fi
od:
R; # Robert Israel, Aug 04 2023

Mathematica

s={4}; a=4; Do[a=a+1; While[PrimeOmega[a]!=2, a=a+2]; AppendTo[s, a], {100}]; s (* Zak Seidov, Feb 12 2015 *)

Prog

(PARI)s=[4]; a=4; for(k=1, 100, a=a+1; while(2<>bigomega(a), a=a+2); s=concat(s, a)); s \\ Zak Seidov, Feb 12 2015
(Sage)
A=[4]
for x in [2..314]:
    if x % 2 != A[-1] % 2 and is_prime(x//prime_divisors(x)[0]):
        A.append(x) # Tom Edgar, Feb 12 2015

Crossrefs

Cf. A001358.

Sequence in context: A139558 A219556 A110602 * A122635 A191912 A191911

Adjacent sequences: A254920 A254921 A254922 * A254924 A254925 A254926

Keyword

nonn

Author

Zak Seidov, Feb 10 2015

Status

approved