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.
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
KEYWORD
nonn,base
AUTHOR
Davide Rotondo, Jul 31 2020
EXTENSIONS
More terms from Amiram Eldar, Jul 31 2020
STATUS
approved