A379929 Numbers that have the same number of prime factors, counted with multiplicity, as there are runs in their base-10 representation.

2, 3, 5, 7, 10, 11, 14, 15, 21, 25, 26, 34, 35, 38, 39, 46, 49, 51, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 102, 105, 115, 118, 119, 122, 124, 125, 130, 133, 138, 147, 148, 153, 154, 155, 164, 165, 166, 170, 171, 172, 174, 175, 177, 182, 186, 190, 195, 207, 212, 221, 226, 230, 231

Offset

1,1

Comments

Numbers k such that A001222(k) = A043562(k).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(5) = 10 is a term because 10 has two runs (1 and 0) and two prime factors, 2 and 5.

Maple

filter:= proc(n) local L; L:= convert(n, base, 10); nops(L) - numboccur(0, L[2..-1]-L[1..-2]) = numtheory:-bigomega(n) end proc:
select(filter, [$1..1000]);

Mathematica

A379929Q[n_] := PrimeOmega[n] == Length[Split[IntegerDigits[n]]];
Select[Range[300], A379929Q] (* Paolo Xausa, Jan 08 2025 *)

Prog

(Python)
from sympy import primeomega
def ok(n): return primeomega(n) == len(s:=str(n)) - sum(1 for i in range(1, len(s)) if s[i-1] == s[i])
print([k for k in range(1, 232) if ok(k)]) # Michael S. Branicky, Jan 08 2025

Crossrefs

Cf. A001222, A043562, A379930, A379931.

Sequence in context: A266679 A285257 A317407 * A191211 A263133 A346592

Adjacent sequences: A379926 A379927 A379928 * A379930 A379931 A379932

Keyword

nonn,base

Author

Robert Israel, Jan 06 2025

Status

approved