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A292941
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a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 6)].
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8
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0, 1, 2, 2, 4, 4, 9, 4, 4, 8, 18, 8, 37, 18, 8, 8, 74, 8, 149, 16, 16, 36, 298, 16, 9, 74, 8, 36, 596, 16, 1193, 16, 36, 148, 16, 16, 2387, 298, 72, 32, 4774, 32, 9549, 72, 16, 596, 19098, 32, 19, 18, 148, 148, 38196, 16, 33, 72, 296, 1192, 76392, 32, 152785, 2386, 32, 32, 72, 72, 305571, 296, 596, 32, 611142, 32, 1222285, 4774, 16, 596, 32
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OFFSET
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1,3
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COMMENTS
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Base-2 expansion of a(n) encodes the steps where numbers of the form 6k+1 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n. An exception is the most significant bit of a(n) which corresponds with the final 1, but is shifted one bit-position towards right (less significant end).
The AND - XOR formulas just restate the fact that J(-3|n) = J(-1|n)*J(3|n), as the Jacobi-symbol is multiplicative (also) with respect to its upper argument.
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LINKS
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FORMULA
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a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 6)], where the last part of the formula is Iverson bracket, giving 1 only if n is of the form 6k+1, and 0 otherwise.
Also, for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 2)]*[J(-3|n) = 1], where J is the Jacobi-symbol.
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PROG
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(Scheme) (define (A292941 n) (if (<= n 2) (- n 1) (+ (if (= 1 (modulo n 6)) 1 0) (* 2 (A292941 (A252463 n))))))
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CROSSREFS
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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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