A027856 Dan numbers: numbers m of the form 2^j * 3^k such that m +- 1 are twin primes.

4, 6, 12, 18, 72, 108, 192, 432, 1152, 2592, 139968, 472392, 786432, 995328, 57395628, 63700992, 169869312, 4076863488, 10871635968, 2348273369088, 56358560858112, 79164837199872, 84537841287168, 150289495621632, 578415690713088, 1141260857376768

Offset: 1

Author

Richard C. Schroeppel

Keywords

• nonn

Comments

Special twin prime averages (A014574).

Intersection of A014574 and A003586. - Jeppe Stig Nielsen, Sep 05 2017

Examples

			a(14) = 243*4096 = 995328 and {995327, 995329} are twin primes.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..62 (terms < 10^1000, first 55 terms from Donovan Johnson)

Crossrefs

Cf. A014574, A060211, A078883, A078884.

Cf. also A002822, A033845, A058383, A003586.

Programs

Mathematica

Select[#, Total@ Boole@ Map[PrimeQ, # + {-1, 1}] == 2 &] &@ Select[Range[10^7], PowerMod[6, #, #] == 0 &] (* Michael De Vlieger, Dec 31 2016 *)
seq[max_] := Select[Sort[Flatten[Table[2^i*3^j, {i, 1, Floor[Log2[max]]}, {j, 0, Floor[Log[3, max/2^i]]}]]], And @@ PrimeQ[# + {-1, 1}] &]; seq[2*10^15] (* Amiram Eldar, Aug 27 2024 *)

Formula

a(n) = A078883(n) + 1 = A078884(n) - 1. - Amiram Eldar, Aug 27 2024

Extensions

Offset corrected by Donovan Johnson, Dec 02 2011

Entry revised by N. J. A. Sloane, Jan 01 2017