A110873 -id:A110873 - cp's OEIS frontend

A055469 Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers).

2, 7, 11, 29, 37, 67, 79, 137, 191, 211, 277, 379, 631, 821, 947, 991, 1129, 1327, 1597, 1831, 2017, 2081, 2347, 2557, 2851, 2927, 3571, 3917, 4561, 4657, 4951, 5051, 5779, 6217, 6329, 8647, 8779, 9181, 9871, 11027, 12721, 13367, 14029, 14197, 14879

Offset: 1

Henry Bottomley, Jun 27 2000

Also primes of the form (n^2 + 7)/8. - Ray Chandler, Oct 08 2005
q=2 and q=5 are the only primes values such that q+1 is a triangular number because 8q+9 is a square for 2 and 5 only. - Benoit Cloitre, Apr 05 2002
n such that A000010(n) = A000217(k). - Giovanni Teofilatto, Jan 29 2010
It is conjectured that this sequence is infinite. - Daniel Forgues, Apr 21 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A000124, A000217, A067186, A110872, A110873, A129545.

Select[Table[(n^2 + 7)/8, {n, 400}], PrimeQ] (* Ray Chandler, Oct 08 2005 *)
Select[Accumulate[Range[400]]+1,PrimeQ] (* Harvey P. Dale, May 14 2022 *)

forprime(p=2,10^5, if ( issquare(8*p-7), print1(p, ", "))) \\ Joerg Arndt, Jul 14 2012

list(lim)=my(v=List(),p); forstep(s=3,sqrtint(lim\1*8-7),2, if(isprime(p=(s^2+7)/8), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, May 05 2020

a(n) = A000124(A067186(n)) = (A110873(n) + 7)/8. - Ray Chandler, Oct 08 2005

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

Original entry on oeis.org

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

Joseph L. Pe, Feb 19 2002

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".

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

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

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

Cf. A000124, A055469, A110872, A110873.

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

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

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

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

Edited by Robert G. Wilson v, Feb 19 2002

A110872 Numbers n such that (n^2+7)/8 is prime.

Original entry on oeis.org

3, 7, 9, 15, 17, 23, 25, 33, 39, 41, 47, 55, 71, 81, 87, 89, 95, 103, 113, 121, 127, 129, 137, 143, 151, 153, 169, 177, 191, 193, 199, 201, 215, 223, 225, 263, 265, 271, 281, 297, 319, 327, 335, 337, 345, 351, 359, 369, 375, 401, 407, 415, 417, 423, 439, 447

Offset: 1

Giovanni Teofilatto, Sep 18 2005

nonn

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A055469, A067186, A110873.

Select[Range[300], PrimeQ[(#^2 + 7)/8] &] (* Ray Chandler, Oct 08 2005 *)

is(n)=isprime((n^2+7)/8) \\ Charles R Greathouse IV, May 22 2017

a(n) = 2*A067186(n) + 1 = Sqrt(A110873(n)).

Extended by Ray Chandler, Oct 08 2005

cp's OEIS Frontend

A055469 Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers).

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

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A110872 Numbers n such that (n^2+7)/8 is prime.

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