A321590 Smallest number m that is a product of exactly n primes and is such that m-1 and m+1 are products of exactly n-1 primes.

4, 50, 189, 1863, 10449, 447849, 4449249, 5745249, 3606422049, 16554218751, 105265530369, 1957645712385

Offset: 2

Author

Zak Seidov, Nov 13 2018

Keywords

• nonn
• more

Comments

From Jon E. Schoenfield, Nov 15 2018: (Start)

If a(11) is odd, it is 16554218751.

If a(12) is odd, it is 105265530369.

If a(13) is odd, it is 1957645712385. (End)

a(11), a(12), and a(13) are indeed odd. - Giovanni Resta, Jan 04 2019

10^13 < a(14) <= 240455334218751, a(15) <= 2992278212890624. - Giovanni Resta, Jan 06 2019

Examples

			For n = 3, 50 = 2*5*5, and the numbers before and after 50 are 49 = 7*7 and 51 = 3*17.
		

Crossrefs

Cf. A078840.

Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), A069274 (r = 13), A069275(r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20).

Programs

Mathematica

a[n_] := Module[{o={0,0,0}, k=1}, While[o!={n-1,n,n-1}, o=Rest[AppendTo[o,PrimeOmega[k]]]; k++]; k-2]; Array[a,7,2] (* Amiram Eldar, Nov 14 2018 *)

PARI

{for(n=2,10,for(k=2^n,10^12,if(n==bigomega(k) &&
n-1==bigomega(k-1) && n-1==bigomega(k+1),print1(k", ");break())))}

Extensions

a(10) from Jon E. Schoenfield, Nov 14 2018

a(11)-a(13) from Giovanni Resta, Jan 04 2019