A294731 Smallest average of a twin prime pair divisible by the n-th prime, i.e. A090530(n), divided by 6*prime(n).

1, 1, 3, 4, 1, 2, 1, 2, 7, 9, 5, 4, 1, 20, 3, 43, 4, 3, 14, 22, 9, 8, 19, 7, 1, 1, 8, 4, 24, 5, 1, 2, 2, 13, 4, 6, 5, 9, 22, 3, 15, 6, 11, 3, 7, 5, 20, 5, 6, 7, 3, 3, 9, 14, 10, 2, 35, 2, 1, 10, 25, 17, 1, 35, 5, 4, 1, 18, 15, 12, 25, 1, 2, 5

Offset: 3

Author

Hugo Pfoertner, Nov 09 2017

Keywords

• nonn
• changed

Comments

The sequence starts at n=3, because A090530(1)=4 is not divisible by 6*2 and A090530(2)=6 is not divisible by 6*3.

The positions of ones in the sequence are given by A060212, i.e. a(A000720(A060212(n)))=1 for all n>=3.

Examples

			a(5)=3 because 198 is the smallest average of a twin prime pair {197,199} that is divisible by the 5th prime 11: 3 = 198 / (6*11).
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A014574, A060212, A071407, A090530, A182481.

Programs

Mathematica

a[n_] := Module[{p = Prime[n], k = 1}, While[! PrimeQ[6*k*p - 1] || ! PrimeQ[6*k*p + 1], k++]; k]; Array[a, 100, 3] (* Amiram Eldar, Aug 25 2025 *)

Formula

a(n) = A090530(n) / ( 6 * prime(n) ) for n >= 3.

a(n) = A071407(n) / 6. - Amiram Eldar, Aug 25 2025