A263282 Numbers n such that 6n is in A002822 but n is not.

63, 65, 88, 98, 102, 133, 157, 163, 185, 193, 198, 203, 208, 210, 233, 245, 250, 262, 310, 340, 380, 387, 413, 437, 457, 462, 473, 478, 483, 493, 507, 508, 515, 530, 585, 600, 627, 635, 640, 647, 658, 662, 677, 718, 742, 765, 772, 793, 795, 830, 847, 857

Offset

1,1

Comments

To use Dinculescu's terminology (see links): non-ranks n such that 6n is a twin-rank.

Links

Jason Kimberley, Table of n, a(n) for n = 1..27455 (equivalently, a(n) < 10^6).

A. Dinculescu, On Some Infinite Series Related to the Twin Primes, The Open Mathematics Journal, 5 (2012), 8-14.

A. Dinculescu, The Twin Primes Seen from a Different Perspective, The British Journal of Mathematics & Computer Science, 3 (2013), Issue 4, 691-698.

Example

Take n = 63; then 6n = 378 and 36n = 2268; now 379, 2267, and 2269 are prime, but 377 = 13 x 29.

Mathematica

s = Select[Range@ 5184, PrimeQ[6 # - 1] && PrimeQ[6 # + 1] &]; Select[s, IntegerQ[#/6] && ! MemberQ[s, #/6] &]/6 (* Michael De Vlieger, Oct 13 2015, after N. J. A. Sloane at A002822 *)

Prog

(Magma) IsInA2822:=func<n|IsPrime(6*n-1)and IsPrime(6*n+1)>;
[n:n in[1..10^3]|not IsInA2822(n)and IsInA2822(6*n)];

Crossrefs

Cf. A002822.

Sequence in context: A112816 A296875 A346803 * A295695 A045271 A198294

Adjacent sequences: A263279 A263280 A263281 * A263283 A263284 A263285

Keyword

nonn,easy

Author

Jason Kimberley, Oct 13 2015

Status

approved