A297772 Number of distinct runs in base-4 digits of n.

1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 3, 3, 2, 1, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 2, 1, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2, 1, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 2, 1, 2

Offset: 1

Author

Clark Kimberling, Jan 27 2018

Keywords

• nonn
• base
• easy

Comments

Every positive integers occurs infinitely many times. See A297770 for a guide to related sequences.

Examples

			123456 in base-4: 1,3,2,0,2,1,0,0,0; seven runs, of which 5 are distinct, so that a(123456) = 5.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A043556 (number of runs, not necessarily distinct), A297770 (distinct runs in base 2).

Programs

Mathematica

b = 4; s[n_] := Length[Union[Split[IntegerDigits[n, b]]]]
Table[s[n], {n, 1, 200}]

PARI

apply( {A297772(n)=my(r=Vec(0, 4), c); while(n, my(d=bitand(n,3),  L=valuation(n+if(d==3, 1, d==2, n\2+1, d, n<<1+1), if(d==2, 2, 4))); d==2 && L\/=2; !bittest(r[1+d], L) && c++ && r[1+d] += 1<>=2*L); c}, [0..99]) \\ M. F. Hasler, Jul 15 2024

Python

from itertools import groupby
from sympy.ntheory import digits
def A297772(n): return len(set(map(lambda x:tuple(x[1]),groupby(sympydigits(n,4)[1:])))) # Chai Wah Wu, Jul 13 2024