A076205 Numbers n such that 30*n+{1,7,11,13,17,19,23,29} are all composite.

360, 523, 654, 941, 1020, 1047, 1064, 1136, 1188, 1213, 1264, 1280, 1343, 1355, 1445, 1477, 1515, 1526, 1530, 1533, 1582, 1623, 1652, 1693, 1842, 1900, 1960, 2018, 2039, 2129, 2208, 2280, 2309, 2332, 2406, 2413, 2440, 2499, 2539, 2622, 2633, 2650, 2657

Offset: 1

Author

Donald S. McDonald, Nov 02 2002

Keywords

• easy
• nonn

References

• H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 141.

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..6829 (terms < 100000)

Crossrefs

Cf. A005776, A007775, A100418-A100423.

Programs

Magma

[ n: n in [0..3000] | forall{ q: q in [1, 7, 11, 13, 17, 19, 23, 29] | not IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011

Mathematica

Select[Range[3000],AllTrue[30#+{1,7,11,13,17,19,23,29},CompositeQ]&] (* Harvey P. Dale, Jan 06 2022 *)

PARI

{cav(mx)= local(wp=[1,7,11,13,17,19,23,29],v=[],i,j,m); for(k=1,mx, i=k*30;j=1;m=1;while(m&&(j<9),m=!isprime(i+wp[j]);j+=1);if(m,v=concat(v,k))); return(v)}

Extensions

More terms from Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004

Edited by Don Reble, Nov 17 2005

Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar