A055670 a(n) = prime(n) - (-1)^prime(n).

1, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284

Offset: 1

Author

N. J. A. Sloane, Jun 09 2000

Keywords

• nonn
• easy
• nice

Comments

Number of right-inequivalent prime Hurwitz quaternions of norm p, where p = n-th rational prime (indexed by A000040).

Two primes are considered right-equivalent if they differ by right multiplication by one of the 24 units. - N. J. A. Sloane

Start of n-th run of consecutive nonprime numbers. Since 2 is the only even prime, for all other prime numbers the expression "- (-1)^(n-th prime)" works out to "+ 1." - Alonso del Arte, Oct 18 2011

Examples

			a(1) = 2 - (-1)^2 = 1, a(2) = 3 - (-1)^3 = 4.
		

References

• L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.
• Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology, Dover, New York, 1978, page 134.

Links

• Shawn A. Broyles, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000040, A006093.

Cf. A055669-A055672.

a(n) = A083503(p) for n>1.

Programs

Mathematica

Join[{1},Prime[Range[2,70]]+1] (* Harvey P. Dale, Oct 29 2013 *)

Formula

a(n) = prime(n)+1 = A008864(n) for n >= 2. a(n) = A055669(n)/24.

Extensions

More terms from David W. Wilson, May 02 2001

I would also like to get the sequences of inequivalent prime Hurwitz quaternions, where two primes are considered equivalent if they differ by left or right multiplication by one of the 24 units. This will give two more sequences, analogs of A055670 and A055672.

Edited by N. J. A. Sloane, Aug 16 2009