A185145 Smallest average of twin prime pairs s such that n*s is also average of twin prime pairs.

4, 6, 4, 18, 6, 12, 6, 30, 12, 6, 18, 6, 150, 30, 4, 12, 6, 4, 12, 12, 42, 30, 6, 18, 6, 12, 4, 270, 12, 6, 42, 6, 6, 30, 12, 12, 180, 6, 60, 6, 30, 150, 30, 30, 4, 18, 6, 4, 18, 12, 42, 6, 150, 30, 12, 60, 4, 6, 18, 4, 462, 180, 1230, 18, 30, 108, 60, 180, 12

Offset: 1

Author

Manuel Valdivia, Mar 12 2012

Keywords

• nonn

Comments

Probably for all n>1 and also for all average s there are at least an average n*s. Note that this is equivalent to the Twin Prime Conjecture. Verified n to 10^7. First consecutive averages: 4 to 34260.

Examples

			A014574(12) = 150, then 13*150 = 1950 = A014574(60).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A066388, A014574.

Programs

Mathematica

t=Select[Table[Prime[n] + 1, {n, 10^4}], PrimeQ[#1 + 1] & ]; Table[s:=t[[m]]; m=1; While[!PrimeQ[n*s-1] || !PrimeQ[n*s+1], m++]; s, {n,1,100}]

Formula

a(n) = A014574(j) if n*A014574(j) = A014574(k).