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

1,2

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

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A000040, A006093.

Cf. A055669-A055672.

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

Sequence in context: A175088 A275671 A370745 * A141096 A089257 A113451

Adjacent sequences: A055667 A055668 A055669 * A055671 A055672 A055673

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jun 09 2000

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

Status

approved