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A256187
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First differences of Per Nørgård's "infinity sequence" A004718.
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2
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1, -2, 3, -1, -1, -2, 5, -4, 3, -2, 1, 1, -3, -2, 7, -3, -1, -2, 5, -3, 1, -2, 3, -4, 5, -2, -1, 3, -5, -2, 9, -6, 3, -2, 1, 1, -3, -2, 7, -4, 1, -2, 3, -1, -1, -2, 5, -1, -3, -2, 7, -5, 3, -2, 1, -4, 7, -2, -3, 5, -7, -2, 11, -5, -1, -2, 5, -3, 1, -2, 3, -4
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Per Nørgård's surname is also written as Noergaard;
a(n) != 0, as A004718 is non-repetitive;
for all integers k > 0, there exist infinitely many m such that abs(a(m)) = k, see link.
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LINKS
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MATHEMATICA
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(* b = A004718 *) b[0] = 0; b[n_?EvenQ] := b[n] = -b[n/2]; b[n_] := b[n] = b[(n-1)/2] + 1;
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PROG
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(Haskell)
a256187 n = a256187_list !! n
a256187_list = zipWith (-) (tail a004718_list) a004718_list
(Python)
from itertools import groupby
c, d = 0, 0
for k, g in groupby(bin(n+1)[2:]):
c = c+len(list(g)) if k == '1' else (-c if len(list(g))&1 else c)
for k, g in groupby(bin(n)[2:]):
d = d+len(list(g)) if k == '1' else (-d if len(list(g))&1 else d)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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