A363786 a(0) = 2. For n >= 1, a(n) is the least prime p such that a(n-1) + p has n prime factors counted with multiplicity.

2, 3, 3, 5, 11, 37, 59, 229, 347, 421, 3163, 4517, 1627, 26021, 14939, 34213, 64091, 378277, 14939, 3392933, 146011, 6931877, 8796763, 37340581, 25573979, 238667173, 113654363, 1018807717, 491141723, 4743349669, 8544205403, 10246276517, 491141723

Offset

0,1

Links

Table of n, a(n) for n=0..32.

Formula

A001222(a(n-1) + a(n)) = n.

Example

a(5) = 37 because a(4) + 37 = 48 = 2^4*3 has 5 prime factors counted with multiplicity.

Maple

R:= 2: t:= 2:
for n from 1 to 30 do
  p:= 1:
  do p:= nextprime(p)
  until numtheory:-bigomega(t+p) = n;
  R:= R, p;
  t:= p;
od:
R;

Mathematica

s={2}; Do[p=2; While[PrimeOmega[s[[-1]]+p]!=
k, p=NextPrime[p]]; Print[p]; AppendTo[s, p], {k, 1, 50}];

Crossrefs

Cf. A001222, A357713.

Sequence in context: A326053 A296083 A294285 * A359033 A064339 A174010

Adjacent sequences: A363783 A363784 A363785 * A363787 A363788 A363789

Keyword

nonn

Author

Zak Seidov and Robert Israel, Jun 21 2023

Status

approved