A169643 - OEIS

%I #30 Jun 12 2026 22:47:04

%S 1,2,6,10,19,28,42,51,75,79,104,114,138,148,152,178,187,212,221,247,

%T 278,338,348,372,423,465,490,504,525,539,669,679,683,709,729,848,858,

%U 873,883,909,961,1028,1071,1080,1089,1104,1202,1221,1247,1251,1354,1363

%N Numbers k such that neither composite(k)+-1 is composite.

%H Robert Israel, <a href="/A169643/b169643.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A066246(A014574(n)). - _Reinhard Zumkeller_, Apr 06 2010

%e a(1) = 1 because composite(1) - 1 = 3 = prime and composite(1) + 1 = 5 = prime.

%p Comp:= remove(isprime,[$4..2000]): nC:= nops(Comp):

%p select(t -> isprime(Comp[t]-1) and isprime(Comp[t]+1), [$1..nC]); # _Robert Israel_, Oct 21 2024

%t Position[Select[Range[2000],CompositeQ],_?(AllTrue[#+{1,-1},PrimeQ]&),1,Heads->False]// Flatten (* _Harvey P. Dale_, Jan 16 2024 *)

%o (PARI) listA169643(lim) = { my(v=List(),k=1);forcomposite(c=4,lim,if(isprime(c+1)&&isprime(c-1),listput(v,k));k++);Vec(v) }; \\ _Bruce Nye_, Jun 07 2026

%o (Python)

%o from itertools import islice

%o from sympy import nextprime

%o def A169643_gen(): # generator of terms

%o     p, q, c = 2, 3, 1

%o     while True:

%o         if (r:=q-p-1)==1:

%o             yield c

%o         c += r

%o         p, q = q, nextprime(q)

%o A169643_list = list(islice(A169643_gen(),30)) # _Chai Wah Wu_, Jun 07 2026

%Y Cf. A002808, A014574, A066246.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Apr 04 2010

%E Corrected by _Ray Chandler_, Apr 05 2010