A074820 Numbers k such that mu(k) = mu(k+2), where mu is the Möbius function (A008683).

3, 5, 11, 16, 17, 18, 25, 29, 33, 41, 48, 50, 52, 54, 55, 59, 71, 85, 88, 90, 91, 93, 96, 98, 101, 103, 105, 107, 124, 126, 137, 141, 143, 148, 149, 150, 159, 160, 162, 163, 165, 169, 179, 183, 185, 191, 193, 195, 196, 197, 198, 201, 203, 213, 215, 217, 219, 227

Offset: 1

Author

Benoit Cloitre, Sep 08 2002

Keywords

• nonn

Comments

a(n) seems to be asymptotic to c*n with c near 3.73. Probably c = 1/(3A/2 + 1 - 12/Pi^2) ~ 3.729994018, where A ~ 0.322634099 is the product over all primes p of 1 - 2/p^2.

Examples

			3 is a term since mu(3) = mu(5) = -1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008683, A064148.

Programs

Mathematica

Select[Range[230], MoebiusMu[ # ]==MoebiusMu[ #+2]&]
Flatten[Position[Partition[MoebiusMu[Range[250]],3,1],?(#[[1]]==#[[3]]&),{1},Heads->False]] (* _Harvey P. Dale, Mar 08 2015 *)

Extensions

Edited by Dean Hickerson, Sep 10 2002