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A373745
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Maximum length of a run of alternating bits in the base-2 representation of prime(n).
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1
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2, 1, 3, 1, 3, 3, 2, 2, 3, 3, 1, 4, 4, 5, 3, 5, 3, 3, 2, 2, 3, 2, 4, 3, 2, 4, 2, 5, 3, 2, 1, 2, 3, 4, 6, 4, 3, 4, 4, 5, 3, 5, 3, 2, 4, 2, 4, 3, 2, 4, 4, 3, 2, 3, 2, 2, 3, 2, 6, 2, 3, 4, 2, 3, 2, 3, 4, 6, 5, 5, 3, 3, 3, 5, 3, 3, 4, 3, 3, 2, 4, 4, 5, 3, 3, 3, 2, 3, 3, 2, 4, 3, 2, 5
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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149 = prime(35) = 10010101_2 has two alternating bit runs of lengths 2 and 6: 10_010101, and thus a(35) = 6.
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MAPLE
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b:= n-> `if`(n<2, [n$2], (f-> (t-> [t, max(t, f[2])])(
`if`(n mod 4 in {0, 3}, 1, f[1]+1)))(b(iquo(n, 2)))):
a:= n-> b(ithprime(n))[2]:
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PROG
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(Python)
from sympy import prime
s = bin(prime(n))[2:]
return next(i for i in range(len(s), 0, -1) if ('01'*(i+1>>1))[:i] in s or ('10'*(i+1>>1))[:i] in s) # Chai Wah Wu, Jul 10 2024
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CROSSREFS
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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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