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 A185145 Smallest average of twin prime pairs s such that n*s is also average of twin prime pairs. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 20 10:13 EDT 2019. Contains 324234 sequences. (Running on oeis4.)