A377185 - OEIS

%I #22 Nov 18 2024 17:14:24

%S 18,30,42,60,72,138,180,198,240,312,420,462,618,660,882,1032,1152,

%T 1230,1290,1320,1482,1722,1878,2592,2688,2970,3120,3168,3300,3330,

%U 3360,3390,3528,3540,3672,4002,4128,4482,5280,5418,5502,6660,6690,6780,7350,7590,7758,8010,8088,8820,9042

%N Average of twin prime pairs A014574 such that the largest odd divisor of the average is the midpoint of the cousin prime pairs A087679.

%H James C. McMahon, <a href="/A377185/b377185.txt">Table of n, a(n) for n = 1..10000</a>

%e 18 is in this sequence because:

%e (a) 18 is average of twin prime pair {17, 19};

%e (b) the largest odd divisor of 18 is 9;

%e (c) 9 is the midpoint of the cousin prime pair {7, 11}.

%t lod[m_]:=Select[Divisors[m+1],OddQ][[-1]];Select[Prime[Range[1130]],PrimeQ[#+2]&&PrimeQ[lod[#]-2]&&PrimeQ[lod[#]+2]&]+1 (* _James C. McMahon_, Nov 17 2024 *)

%o (Magma) [n: n in [4..10^4] | IsPrime(n-1) and IsPrime(n+1) and IsPrime((n div 2^Valuation(n, 2))-2) and IsPrime((n div 2^Valuation(n, 2))+2)];

%Y Cf. A000265, A014574, A087679.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 19 2024