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

Author

Zak Seidov and Robert Israel, Jun 21 2023

Keywords

• nonn

Examples

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

Crossrefs

Cf. A001222, A357713.

Programs

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}];

Formula

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