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A324883
a(n) = 1 if A055396(n) < A324885(n), otherwise 0.
5
0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1
OFFSET
1
COMMENTS
Difference between the 2-adic valuations of A324819(n) and A324866(n).
Of the first 10000 terms, 2540 are 0's and 7460's are 1's. Even n such that a(n) = 0 are rare: 2, 10, 50, 98, 154, 266, 374, 598, 770, 1054, 1250, 1558, 2162, 2662, 3422, 4154, 5390, 5402, 6578, 6806, 8342, 8918, 9682 are all such n less than 10001.
FORMULA
a(n) = A324884(n) - A324882(n).
For n > 1, a(n) = A007814(A324819(n)) - A007814(A324866(n)).
For n > 1, a(n) = A324903(A156552(n)).
a(p) = 0 for all primes p.
PROG
(PARI)
\\ Needs code also from A323243.
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A324819(n) = bitor(2*A156552(n), A323243(n));
A324866(n) = { my(k=A156552(n)); bitor(k, (A323243(n)-k)); };
A001511ext(n) = if(!n, n, sign(n)*(1+valuation(n, 2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
A324882(n) = A001511ext(A324866(n));
A324884(n) = A001511ext(A324819(n));
A324883(n) = (A324884(n)-A324882(n));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 28 2019
STATUS
approved