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A344851
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a(n) = (n^2) mod (2^A070939(n)).
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1
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0, 1, 0, 1, 0, 1, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 16, 25, 4, 17, 0, 17, 4, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 0, 17, 36, 57, 16, 41, 4, 33, 0, 33, 4, 41, 16, 57, 36, 17, 0, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
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OFFSET
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0,7
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COMMENTS
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Informally, if n has w binary digits, a(n) is obtained by keeping the w final binary digits of n^2.
For n > 0, a(n) is the final digit of n^2 in base A062383(n).
This sequence has interesting graphical features (see illustration in Links section).
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LINKS
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FORMULA
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a(n) = 0 iff n = 0 or n > 1 and n belongs to A116882.
a(2^k + m) = a(2^(k+1)-m) for any k > 0 and m = 0..2^k.
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EXAMPLE
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For n = 42:
- a(42) = (42^2) mod (2^6) = 1764 mod 64 = 36.
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MATHEMATICA
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PROG
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(PARI) a(n) = (n^2) % 2^#binary(n)
(Python)
def a(n): return (n**2) % (2**n.bit_length())
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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