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A297771
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Number of distinct runs in base-3 digits of n.
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3
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1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 2, 1, 2, 2, 3, 3, 3, 3, 4, 3, 3, 3, 2
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OFFSET
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1,3
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COMMENTS
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Every positive integers occurs infinitely many times. See A297770 for a guide to related sequences.
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LINKS
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FORMULA
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EXAMPLE
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1040 in base-3: 1,1,0,2,1,1,2; five runs, of which 3 are distinct, so that a(1040) = 3.
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MATHEMATICA
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b = 3; s[n_] := Length[Union[Split[IntegerDigits[n, b]]]]
Table[s[n], {n, 1, 200}]
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PROG
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(Python)
from itertools import groupby
from sympy.ntheory import digits
def A297771(n): return len(set(map(lambda x:tuple(x[1]), groupby(digits(n, 3)[1:])))) # Chai Wah Wu, Jul 13 2024
(PARI) apply( {A297771(n)=my(r=Vec(0, 3), c); while(n, my(d=n%3, L=valuation(n+if(d>1, 1, d, n+1), 3)); !bittest(r[1+d], L) && c++ && r[1+d] += 1<<L; n\=3^L); c}, [0..99]) \\ M. F. Hasler, Jul 13 2024
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CROSSREFS
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Cf. A043555 (number of runs, not necessarily distinct), A297770 (this for base 2).
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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