OFFSET
1,1
COMMENTS
A counterpart to A002822, which generates twin primes.
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
LINKS
Zak Seidov, Table of n, a(n) for n = 1..5000
FORMULA
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
EXAMPLE
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).
MAPLE
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
MATHEMATICA
Select[Range[200], !PrimeQ[6#-1]&&!PrimeQ[6#+1]&] (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
Select[Range[300], AllTrue[6#+{1, -1}, CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 15 2015 *)
Select[Range@ 300, Times @@ Boole@ Map[CompositeQ, 6 # + {1, -1}] > 0 &] (* Michael De Vlieger, Sep 14 2016 *)
PROG
(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
(MATLAB)
i=1:10000;
Q1 = 6*i-1;
Q2 = 6*i+1;
Q = union(Q1, Q2);
P = primes(max(Q));
AT = setxor(Q, P);
f = 0;
for j=1:numel(AT);
K = AT(j);
K2 = K+2;
z = ismember(K2, AT);
if z == 1;
f = f+1;
ATR(f, :) = K + 1;
end
end
m6 = ATR./6;
% Jesse H. Crotts, Sep 05 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Apr 09 2001
EXTENSIONS
More terms from James A. Sellers, Apr 11 2001
STATUS
approved