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.

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

Offset: 1

Author

Davide Rotondo, Jul 31 2020

Keywords

• nonn
• base

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.

Examples

			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... .
		

Crossrefs

Cf. A006970 (Euler pseudoprimes, a subsequence), A003592, A334834.

Programs

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 *)

Extensions

More terms from Amiram Eldar, Jul 31 2020