login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
0
4, 50, 189, 1863, 10449, 447849, 4449249, 5745249, 3606422049, 16554218751, 105265530369, 1957645712385
OFFSET
2,1
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
EXAMPLE
For n = 3, 50 = 2*5*5, and the numbers before and after 50 are 49 = 7*7 and 51 = 3*17.
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 *)
PROG
(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())))}
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).
Sequence in context: A356082 A319139 A254543 * A274872 A189894 A275291
KEYWORD
nonn,more
AUTHOR
Zak Seidov, Nov 13 2018
EXTENSIONS
a(10) from Jon E. Schoenfield, Nov 14 2018
a(11)-a(13) from Giovanni Resta, Jan 04 2019
STATUS
approved