A027856 - OEIS

%I #44 Aug 27 2024 09:14:50

%S 4,6,12,18,72,108,192,432,1152,2592,139968,472392,786432,995328,

%T 57395628,63700992,169869312,4076863488,10871635968,2348273369088,

%U 56358560858112,79164837199872,84537841287168,150289495621632,578415690713088,1141260857376768

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

%C Special twin prime averages (A014574).

%C Intersection of A014574 and A003586. - _Jeppe Stig Nielsen_, Sep 05 2017

%H Ray Chandler, <a href="/A027856/b027856.txt">Table of n, a(n) for n = 1..62</a> (terms < 10^1000, first 55 terms from Donovan Johnson)

%F a(n) = A078883(n) + 1 = A078884(n) - 1. - _Amiram Eldar_, Aug 27 2024

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

%t Select[#, Total@ Boole@ Map[PrimeQ, # + {-1, 1}] == 2 &] &@ Select[Range[10^7], PowerMod[6, #, #] == 0 &] (* _Michael De Vlieger_, Dec 31 2016 *)

%t 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 *)

%Y Cf. A014574, A060211, A078883, A078884.

%Y Cf. also A002822, A033845, A058383, A003586.

%K nonn

%O 1,1

%A Richard C. Schroeppel

%E Offset corrected by _Donovan Johnson_, Dec 02 2011

%E Entry revised by _N. J. A. Sloane_, Jan 01 2017