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

1,1

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.

Links

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

Formula

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

Example

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

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}]

Crossrefs

Cf. A066388, A014574.

Sequence in context: A019245 A019191 A321355 * A258836 A292387 A208540

Adjacent sequences: A185142 A185143 A185144 * A185146 A185147 A185148

Keyword

nonn

Author

Manuel Valdivia, Mar 12 2012

Status

approved