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

0,2

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?

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Formula

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

Example

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.

Prog

(PARI) lista(n)={my(L=List(), p=1, k=0); while(#L<=n, k++; my(t=bigomega(k)); if(abs(t-p)==1, listput(L, k); p=t)); Vec(L)} \\ Andrew Howroyd, Mar 20 2025

Crossrefs

Cf. A001222 (bigomega), A071192.

Sequence in context: A126424 A164317 A138620 * A260820 A248554 A346993

Adjacent sequences: A382226 A382227 A382228 * A382230 A382231 A382232

Keyword

nonn

Author

Gordon Hamilton, Mar 19 2025

Status

approved