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A227196
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a(n) = first i >= 1 for which the Kronecker symbol K(i,n) is not +1 (i.e., is either 0 or -1), 0 if no such i exists.
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6
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0, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 5, 2, 7, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 7, 2, 5, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3
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OFFSET
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1,2
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COMMENTS
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a(1) = 0, because K(i,1) is 1 for all i. After that, A112046 interleaved with A007395.
All terms beyond a(1) = 0 are prime numbers. Heuristically a(n) is 2 3/4 of the time, 3 1/6 of the time, 5 1/20 of the time, 7 2/105 of the time, etc. The average value is 2.5738775742512.... - Charles R Greathouse IV, Jan 30 2018
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LINKS
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FORMULA
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PROG
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(PARI) a(n) = for(k=1, n, if(kronecker(k, n)<1, return(k)))
for(n=1, 120, print1(a(n), ", "))
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CROSSREFS
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Bisections: A112046 (for odd terms from 3 onward), A007395 (all even terms).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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