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A100714
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Number of runs in binary expansion of A000040(n) (the n-th prime number) for n > 0.
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6
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2, 1, 3, 1, 3, 3, 3, 3, 3, 3, 1, 5, 5, 5, 3, 5, 3, 3, 3, 3, 5, 3, 5, 5, 3, 5, 3, 5, 5, 3, 1, 3, 5, 5, 7, 5, 5, 5, 5, 7, 5, 7, 3, 3, 5, 3, 5, 3, 3, 5, 5, 3, 3, 3, 3, 3, 5, 3, 7, 5, 5, 7, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 7, 5, 3, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 3, 5, 5, 3, 5, 3, 3, 5, 3, 3, 3, 5, 5, 5, 5, 7, 5, 5, 5
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OFFSET
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1,1
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COMMENTS
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Record values of a(n) = 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, ... are set at the indices n = 1, 3, 12, 35, 121, 355, 1317, 4551, 15897, 56475, 197249, 737926, ... - R. J. Mathar, Mar 02 2007
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LINKS
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FORMULA
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EXAMPLE
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a(5)=3 because A000040(5) = 11_10 = 1011_2, which splits into three runs ({1}, {0}, {1,1}).
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MATHEMATICA
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Table[Length[Split[IntegerDigits[Prime[n], 2]]], {n, 1, 128}]
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PROG
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(Python)
from sympy import prime
def a(n): return ((p:=prime(n))^(p>>1)).bit_count()
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004
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STATUS
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approved
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