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

1,4

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(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
(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<<L; n>>=2*L); c}, [0..99]) \\ M. F. Hasler, Jul 15 2024

Crossrefs

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

Sequence in context: A219025 A270746 A043531 * A043556 A230643 A344117

Adjacent sequences: A297769 A297770 A297771 * A297773 A297774 A297775

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 27 2018

Status

approved