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A067186 Numbers n such that C(n) = (n^2 + n + 2)/2 is prime. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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".

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A000124, A055469, A110872, A110873.

Sequence in context: A058235 A107819 A300950 * A133675 A173467 A050122

Adjacent sequences:  A067183 A067184 A067185 * A067187 A067188 A067189

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Feb 19 2002

EXTENSIONS

Edited by Robert G. Wilson v, Feb 19 2002

STATUS

approved

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)