A382229 a(0) = 1; thereafter a(n) is the next larger number that compared to the previous term differs by +-1 in the number of prime factors counted with multiplicity.

1, 2, 4, 5, 6, 7, 9, 11, 14, 17, 21, 23, 25, 27, 33, 37, 38, 41, 46, 47, 49, 50, 51, 52, 54, 63, 65, 66, 69, 70, 74, 75, 77, 78, 81, 92, 93, 97, 106, 107, 111, 113, 115, 116, 118, 124, 126, 130, 132, 138, 140, 147, 150, 153, 155, 157, 158, 163, 166, 167, 169, 170, 177, 179, 183, 186

Offset: 0

Author

Gordon Hamilton, Mar 19 2025

Keywords

• nonn

Comments

a(n+1) is the least integer k > a(n) such that abs(bigomega(k) - bigomega(a(n))) = 1.

Do an infinite number of primes appear in the sequence?

Examples

			Example: 52 = 2*2*13 is a term. 53 is not a term because it has -2 prime factors compared to 52. 54 = 2*3*3*3 is a term because it has +1 factor compared to 52. 55 = 5*11 is not a term because it has -2 factors compared to 54. 56 is not a term because it has the same number of factors as 54.
		

Crossrefs

Cf. A001222 (bigomega), A071192.

Programs

PARI

lista(n)={my(L=List(), p=0, k=1); while(#LAndrew Howroyd, Mar 20 2025

Formula

a(n) = A071192(a(n-1)). - Pontus von Brömssen, Mar 21 2025