A067186 Numbers n such that C(n) = (n^2 + n + 2)/2 is prime.

1, 3, 4, 7, 8, 11, 12, 16, 19, 20, 23, 27, 35, 40, 43, 44, 47, 51, 56, 60, 63, 64, 68, 71, 75, 76, 84, 88, 95, 96, 99, 100, 107, 111, 112, 131, 132, 135, 140, 148, 159, 163, 167, 168, 172, 175, 179, 184, 187, 200, 203, 207, 208, 211, 219, 223, 228, 236, 240, 251, 260

Offset: 1

Author

Joseph L. Pe, Feb 19 2002

Keywords

• easy
• nonn

Comments

C(n) gives the maximum number of pieces in which a circular disc can be cut with n slices (A000124). C. Pickover calls the C(n)s "cake integers".

Examples

			C(7) = (7^2 + 7 + 2)/2 = 29, a prime, so 7 is a term of the sequence.
		

References

• Pickover, C. "Wonders of Numbers", Oxford Univ. Press, 2001; page 158, ch. 65.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Crossrefs

Cf. A000124, A055469, A110872, A110873.

Programs

Magma

[n: n in [1..300] | IsPrime((n^2 + n + 2) div 2)]; // Vincenzo Librandi, Sep 30 2012

Mathematica

Select[ Range[300], PrimeQ[(#^2 + # + 2)/ 2] &]

PARI

is(n)=isprime(n*(n+1)/2+1) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = (A110872(n) - 1)/2. - Ray Chandler, Oct 08 2005

Extensions

Edited by Robert G. Wilson v, Feb 19 2002