|
%I #68 Sep 10 2021 20:34:02
%S 20,24,31,34,36,41,48,50,54,57,69,71,79,86,88,89,92,97,104,106,111,
%T 116,119,130,132,134,136,139,141,145,149,150,154,160,167,171,174,176,
%U 179,180,189,190,191,193,196,201,207,209,211,212,219,222,223,224,225,226
%N Numbers k such that 6*k-1 and 6*k+1 are twin composites.
%C A counterpart to A002822, which generates twin primes.
%C Intersection of A046953 and A046954. - _Michel Marcus_, Sep 27 2013
%C All terms can be expressed as (6ab+a+b OR 6cd-c-d) AND (6xy+x-y) for a,b,c,d,x,y positive integers. Example: 20=6*2*2-2-2 AND 20=6*3*1+3-1. - _Pedro Caceres_, Apr 21 2019
%H Zak Seidov, <a href="/A060461/b060461.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) ~ n. More specifically, there are x - x/log x + O(x/log^2 x) terms of the sequence up to x. - _Charles R Greathouse IV_, Mar 03 2020
%e a(9)=57: the 9th twin composites among the odds are {6*57-1}, {6*57+1}, i.e., (341,343) or (11*31, 7^3).
%p iscomp := proc(n) if n=1 or isprime(n) then RETURN(0) else RETURN(1) fi: end: for n from 1 to 500 do if iscomp(6*n-1)=1 and iscomp(6*n+1)=1 then printf(`%d,`,n) fi: od: # _James A. Sellers_, Apr 11 2001
%t Select[Range[200], !PrimeQ[6#-1]&&!PrimeQ[6#+1]&] (* _Vladimir Joseph Stephan Orlovsky_, Aug 07 2008 *)
%t Select[Range[300],AllTrue[6#+{1,-1},CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 15 2015 *)
%t Select[Range@ 300, Times @@ Boole@ Map[CompositeQ, 6 # + {1, -1}] > 0 &] (* _Michael De Vlieger_, Sep 14 2016 *)
%o (PARI) A060461()={my(maxx=5000); n=1; ctr=0; while(ctr<maxx, if(!isprime(6*n-1)&&!isprime(6*n+1), print1(n,", "); ctr+=1); n+=1); } \\ _Bill McEachen_, Apr 04 2015
%o (MATLAB)
%o i=1:10000;
%o Q1 = 6*i-1;
%o Q2 = 6*i+1;
%o Q = union(Q1,Q2);
%o P = primes(max(Q));
%o AT = setxor(Q,P);
%o f = 0;
%o for j=1:numel(AT);
%o K = AT(j);
%o K2 = K+2;
%o z = ismember(K2,AT);
%o if z == 1;
%o f = f+1;
%o ATR(f,:) = K + 1;
%o end
%o end
%o m6 = ATR./6;
%o % _Jesse H. Crotts_, Sep 05 2016
%Y Cf. A002822, A046953, A046954, A259826.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Apr 09 2001
%E More terms from _James A. Sellers_, Apr 11 2001
|
