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

1,1

Links

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

Example

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].

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

Crossrefs

Cf. A014574, A068525, A294730.

Sequence in context: A093121 A248048 A209298 * A088255 A192083 A068720

Adjacent sequences: A075587 A075588 A075589 * A075591 A075592 A075593

Keyword

nonn

Author

Amarnath Murthy, Sep 26 2002

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.

Status

approved