A368648 Lexicographically earliest increasing sequence of semiprimes such that a(n) + a(n+1) is a semiprime, with a(0) = 4.

4, 6, 9, 25, 26, 39, 46, 49, 57, 58, 65, 69, 74, 85, 93, 94, 111, 115, 122, 143, 146, 155, 159, 187, 194, 201, 202, 205, 206, 209, 213, 214, 237, 265, 278, 287, 299, 323, 326, 329, 358, 365, 381, 382, 403, 415, 427, 451, 454, 469, 482, 497, 501, 502, 505, 537, 542, 559, 562, 573, 581, 586, 591, 611

Offset: 0

Author

Zak Seidov and Robert Israel, Jan 02 2024

Keywords

• nonn

Comments

The only case where two successive terms are even is 4, 6 at the start, since if 2*p and 2*q are semiprimes where p and q are odd primes, 2*p + 2*q is divisible by 4.

Examples

			a(2) = 6 because 6 = 2 * 3 and 4 + 6 = 10 = 2 * 5 are semiprimes.
a(3) = 9 because 9 = 3 * 3 and 6 + 9 = 15 = 3 * 5 are semiprimes.
a(4) = 25 because 25 = 5 * 5 and 9 + 25 = 34 = 2 * 17 are semiprimes.
		

Links

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

Crossrefs

Cf. A001358, A361611.

Programs

Maple

R:= 4: x:= 4: count:= 1:
for y from 5 do
    if numtheory:-bigomega(y) = 2 and numtheory:-bigomega(x+y) = 2 then
      R:= R,y; x:= y; count:= count+1;
      if count = 100 then break fi
    fi
od:
R;