A075590 Smallest number with n distinct prime divisors which is the average of a twin prime pair.

4, 6, 30, 420, 2310, 43890, 1138830, 17160990, 300690390, 15651726090, 239378649510, 12234189897930, 461282657605770, 19835154277048110, 693386350578511590, 37508276737897976010, 3338236629672919864890, 209580878166809177658630, 11465419967969569966774410

Offset: 1

Author

Amarnath Murthy, Sep 26 2002

Keywords

• nonn

Examples

			a(4) = 420 = 2^2*3*5*7, (419,421) is a twin prime pair. (210 = 2*3*5*7, 211 is prime but 209 is composite).
a(8) = 17160990 = 2*3*5*7*11*17*19*23 and 17160989 = p[1100977], 17160991 = p[1100978].
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A014574, A068525, A294730.

Programs

Mathematica

t=Table[0, {10}]; Do[s=Length[FactorInteger[Prime[n]+1]]; If[PrimeQ[Prime[n]+2] && s<11 && t[[s]]==0, t[[s]]=Prime[n]+1], {n, 1, 1200000}]; t

Extensions

More terms from Labos Elemer, Sep 27 2002

Corrected and extended by T. D. Noe, Nov 30 2004. a(9)-a(18) were found by testing all the numbers x with n distinct prime factors, x < 3 prime(n)# and both x-1 and x+1 prime.