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A084953
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Numbers k such that k! is the sum of 4 but no fewer nonzero squares.
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3
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10, 12, 24, 25, 48, 49, 54, 60, 78, 91, 96, 97, 107, 114, 120, 121, 142, 151, 167, 170, 172, 180, 192, 193, 212, 222, 226, 238, 240, 241, 246, 252, 270, 279, 301, 307, 309, 318, 327, 333, 344, 345, 357, 360, 361, 367, 375, 379, 384, 385, 403, 405, 421, 424, 425
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listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is 1/8 (Deshouillers and Luca, 2010). - Amiram Eldar, Jan 11 2021
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LINKS
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FORMULA
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Equivalently, k! is of the form (4^i)*(8*j+7), i >= 0, j >= 0.
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EXAMPLE
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a(1) = 10 because 10! cannot be written as the sum of fewer than 4 squares.
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MATHEMATICA
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Select[Range[500], Mod[#!/4^IntegerExponent[#!, 4], 8] == 7 &] (* Amiram Eldar, Jan 11 2021 *)
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PROG
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See link.
(PARI) isA004215(n)= n\4^valuation(n, 4)%8==7;
(Python 3.10+)
from math import factorial
from itertools import count, islice
def A084953_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:(factorial(n)>>((n-n.bit_count())&-2))&7==7, count(max(startvalue, 1)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Added missing term 357 by Rob Burns, Dec 30 2020
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STATUS
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approved
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