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A336689 Composite numbers k such that the decimal expansion of ((1/2^((k-1)/2))+1)/k or ((1/2^((k-1)/2))-1)/k is finite. 0
15, 25, 75, 125, 175, 325, 341, 375, 425, 561, 625, 645, 1105, 1729, 1875, 1905, 2047, 2465, 3125, 3277, 4033, 4375, 4681, 5461, 6025, 6601, 8125, 8321, 8481, 8625, 9375, 10261, 10585, 10625, 12025, 12801, 15625, 15709, 15841, 16705, 16725, 18705, 25761, 29341 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If (1/2^((k-1)/2))+-1 divided by k results in a finite decimal number, k is prime or pseudoprime.
Euler pseudoprimes: A006970 are a subsequence.
If k is a power of 5, both +1 and -1 result in a finite decimal number.
A composite integer is part of this list, if and only if
(((n-1)!-1)*(1/(2^((n-1)/2)))+1)/n or (((n-1)!-1)*(1/(2^((n-1)/2)))-1)/n results in a finite decimal number.
LINKS
EXAMPLE
15 is a term because ((1/(2^7))+1)/15 = 0.0671875.
9 is not a term because ((1/(2^4))+-1)/9 = 0.11805555... and -0.10416666... .
MATHEMATICA
A003592Q[n_] := n/2^IntegerExponent[n, 2]/5^IntegerExponent[n, 5] == 1; seqQ[n_] := CompositeQ[n] && (A003592Q[Denominator[((1/2^((n-1)/2)) + 1)/n]] || A003592Q[ Denominator[((1/2^((n-1)/2)) - 1)/n]]); Select[Range[1, 30000, 2], seqQ] (* Amiram Eldar, Jul 31 2020 *)
CROSSREFS
Cf. A006970 (Euler pseudoprimes, a subsequence), A003592, A334834.
Sequence in context: A020202 A020300 A032587 * A347375 A062238 A146249
KEYWORD
nonn,base
AUTHOR
Davide Rotondo, Jul 31 2020
EXTENSIONS
More terms from Amiram Eldar, Jul 31 2020
STATUS
approved

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Last modified June 22 20:25 EDT 2024. Contains 373608 sequences. (Running on oeis4.)