A060461 Numbers k such that 6*k-1 and 6*k+1 are twin composites.

20, 24, 31, 34, 36, 41, 48, 50, 54, 57, 69, 71, 79, 86, 88, 89, 92, 97, 104, 106, 111, 116, 119, 130, 132, 134, 136, 139, 141, 145, 149, 150, 154, 160, 167, 171, 174, 176, 179, 180, 189, 190, 191, 193, 196, 201, 207, 209, 211, 212, 219, 222, 223, 224, 225, 226

Offset

1,1

Comments

A counterpart to A002822, which generates twin primes.

Intersection of A046953 and A046954. - Michel Marcus, Sep 27 2013

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

Cf. A002822, A046953, A046954, A259826.

Sequence in context: A108373 A109131 A171696 * A214177 A044996 A347190

Adjacent sequences: A060458 A060459 A060460 * A060462 A060463 A060464

Keyword

nonn

Author

Lekraj Beedassy, Apr 09 2001

Extensions

More terms from James A. Sellers, Apr 11 2001

Status

approved