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

%I A067186 #18 Sep 08 2022 08:45:05
%S A067186 1,3,4,7,8,11,12,16,19,20,23,27,35,40,43,44,47,51,56,60,63,64,68,71,
%T A067186 75,76,84,88,95,96,99,100,107,111,112,131,132,135,140,148,159,163,167,
%U A067186 168,172,175,179,184,187,200,203,207,208,211,219,223,228,236,240,251,260
%N A067186 Numbers n such that C(n) = (n^2 + n + 2)/2 is prime.
%C A067186 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".
%D A067186 Pickover, C. "Wonders of Numbers", Oxford Univ. Press, 2001; page 158, ch. 65.
%H A067186 Vincenzo Librandi, <a href="/A067186/b067186.txt">Table of n, a(n) for n = 1..1000</a>
%H A067186 C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>
%F A067186 a(n) = (A110872(n) - 1)/2. - _Ray Chandler_, Oct 08 2005
%e A067186 C(7) = (7^2 + 7 + 2)/2 = 29, a prime, so 7 is a term of the sequence.
%t A067186 Select[ Range[300], PrimeQ[(#^2 + # + 2)/ 2] &]
%o A067186 (Magma) [n: n in [1..300] | IsPrime((n^2 + n + 2) div 2)]; // _Vincenzo Librandi_, Sep 30 2012
%o A067186 (PARI) is(n)=isprime(n*(n+1)/2+1) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y A067186 Cf. A000124, A055469, A110872, A110873.
%K A067186 easy,nonn
%O A067186 1,2
%A A067186 _Joseph L. Pe_, Feb 19 2002
%E A067186 Edited by _Robert G. Wilson v_, Feb 19 2002