A113752 Smallest number m such that m, m+1 and m+2 have exactly n prime factors (counted with multiplicity).

33, 170, 1274, 15470, 33614, 3145310, 40909374, 668363967, 9864741248, 179199427328, 967461818750, 57938945781248, 597779386906624

Offset: 2

Author

Martin Fuller, Jan 17 2006

Keywords

• nonn
• hard
• more
• changed

Comments

n = A001222(a(n)) = A001222(a(n)+1) = A001222(a(n)+2). Subsequence of A045920.

a(14) <= 1247579465781248. - Donovan Johnson, Jun 12 2013

a(15) > 2 * 10^15. - Toshitaka Suzuki, Aug 31 2025

Examples

			a(6) = 33614 = 2*7*7*7*7*7, a(6)+1 = 3*3*3*3*5*83, a(6)+2 = 2*2*2*2*11*191
		

Crossrefs

Cf. A001222, A045920, A093549, A093550, A115186.

Programs

Mathematica

t = {}; n = 2; m = 1; While[Length[t] < 5, m++; If[n == PrimeOmega[m] == PrimeOmega[m + 1] == PrimeOmega[m + 2], AppendTo[t, m]; n++]]; t (* T. D. Noe, Aug 19 2013 *)

Extensions

a(9)-a(11) from Donovan Johnson, Apr 08 2008

a(12) from Donovan Johnson, Aug 08 2011

a(13) from Jud McCranie, Aug 19 2013

a(14) from Toshitaka Suzuki, Aug 31 2025