A377185 Average of twin prime pairs A014574 such that the largest odd divisor of the average is the midpoint of the cousin prime pairs A087679.

18, 30, 42, 60, 72, 138, 180, 198, 240, 312, 420, 462, 618, 660, 882, 1032, 1152, 1230, 1290, 1320, 1482, 1722, 1878, 2592, 2688, 2970, 3120, 3168, 3300, 3330, 3360, 3390, 3528, 3540, 3672, 4002, 4128, 4482, 5280, 5418, 5502, 6660, 6690, 6780, 7350, 7590, 7758, 8010, 8088, 8820, 9042

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 19 2024

Keywords

• nonn

Examples

			18 is in this sequence because:
(a) 18 is average of twin prime pair {17, 19};
(b) the largest odd divisor of 18 is 9;
(c) 9 is the midpoint of the cousin prime pair {7, 11}.
		

Links

• James C. McMahon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000265, A014574, A087679.

Programs

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)];

Mathematica

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 *)