A361874 a(n) is the least k such that k, k+1 and 2*k+1 all have exactly n prime factors counted with multiplicity.

2, 25, 171, 1592, 37975, 928624, 8412687, 106390624, 2306890624, 37119730112, 429122890624, 23027923554687

Offset

1,1

Comments

From Ray Chandler, Apr 08 2023: (Start)

a(13) <= 2088002787109375.

a(14) <= 7002191787109375.

a(15) <= 100007718212890624.

a(16) <= 4838361918212890624.

a(17) <= 86569490081787109375. (End)

From Ray Chandler, Apr 11 2023: (Start)

a(13) <= 1228742893554687.

a(15) <= 22134455942791167. (End)

Links

Table of n, a(n) for n=1..12.

Example

a(3) = 171 because 171 = 3^2*19, 171 + 1 = 172 = 2^2*43, and 2*171 + 1 = 343 = 7^3 all have 3 prime factors, and 171 is the least number that works.

Maple

f:= proc(n) local x;
for x from 2^n do
  if numtheory:-bigomega(x)=n and numtheory:-bigomega(x+1)=n and numtheory:-bigomega(2*x+1)=n then
    return x
fi od end proc:
map(f, [$1..6]);

Mathematica

a={}; nmax=6; For[n=1, n<=nmax, n++, For[k=1, k>0, k++, If[PrimeOmega[k]==PrimeOmega[k+1]==PrimeOmega[2k+1]==n, AppendTo[a, k]; k=-1]]]; a (* Stefano Spezia, Mar 31 2023 *)

Prog

(PARI) chk(k, n) = (bigomega(k)==n) && (bigomega(k+1)==n) && (bigomega(2*k+1)==n); \\ Michel Marcus, Apr 12 2023

Crossrefs

Cf. A001222.

Sequence in context: A063264 A024533 A220276 * A215298 A094218 A203767

Adjacent sequences: A361871 A361872 A361873 * A361875 A361876 A361877

Keyword

nonn,more

Author

Zak Seidov and Robert Israel, Mar 27 2023

Extensions

a(11) from Michael S. Branicky, Mar 30 2023

a(12) from Martin Ehrenstein, Apr 12 2023

Status

approved