A068638 a(1) = 1, a(n) = smallest distinct composite number such that a(n) + a(k) is a composite number for all k = 1 to n.

1, 8, 14, 20, 24, 25, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 90, 92, 94, 98, 104, 110, 116, 118, 120, 122, 128, 134, 140, 144, 146, 152, 158, 160, 164, 170, 176, 182, 184, 188, 194, 200, 206, 212, 218, 220, 224, 230, 234, 236, 242, 248, 254, 260, 264, 266

Offset: 1

Author

Amarnath Murthy, Feb 27 2002

Keywords

• easy
• nonn

Comments

Conjecture: 25 is the largest odd term of this sequence.

Essentially the same as A025044. - R. J. Mathar, Sep 30 2008

Examples

			a(2) = 8 as for the smaller composite numbers 4 and 6 one gets 4 + 1 = 5 and 6 + 1 = 7, both primes. a(3) = 14 as 1 + 14 = 15 and 8 + 14 = 22 are composite.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025044.

Programs

Mathematica

a1 = {0}; nmax = 266; Do[ If[Select[n + a1, PrimeQ] == {}, AppendTo[a1, n]] , {n, nmax}]; Rest[a1] (* Ray Chandler, Jan 15 2017 *)

Python

from sympy import isprime
from itertools import islice
def agen(start=1): # generator of terms
    alst, k, sums = [0, start], 2, {0} | {start}
    while True:
        yield alst[-1]
        while any(isprime(k+an) for an in alst): k += 1
        alst.append(k)
        k += 1
print(list(islice(agen(), 60))) # Michael S. Branicky, Dec 15 2022

Extensions

More terms from Sascha Kurz, Mar 17 2002

Description clarified by Ray Chandler, Jan 15 2017