A068638 - OEIS

%I #17 Dec 15 2022 09:59:59

%S 1,8,14,20,24,25,26,32,38,44,50,56,62,68,74,80,86,90,92,94,98,104,110,

%T 116,118,120,122,128,134,140,144,146,152,158,160,164,170,176,182,184,

%U 188,194,200,206,212,218,220,224,230,234,236,242,248,254,260,264,266

%N 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.

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

%C Essentially the same as A025044. - _R. J. Mathar_, Sep 30 2008

%H Ray Chandler, <a href="/A068638/b068638.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%o (Python)

%o from sympy import isprime

%o from itertools import islice

%o def agen(start=1): # generator of terms

%o     alst, k, sums = [0, start], 2, {0} | {start}

%o     while True:

%o         yield alst[-1]

%o         while any(isprime(k+an) for an in alst): k += 1

%o         alst.append(k)

%o         k += 1

%o print(list(islice(agen(), 60))) # _Michael S. Branicky_, Dec 15 2022

%Y Cf. A025044.

%K easy,nonn

%O 1,2

%A _Amarnath Murthy_, Feb 27 2002

%E More terms from _Sascha Kurz_, Mar 17 2002

%E Description clarified by _Ray Chandler_, Jan 15 2017