A114963 a(n) = n^2 + 22.

22, 23, 26, 31, 38, 47, 58, 71, 86, 103, 122, 143, 166, 191, 218, 247, 278, 311, 346, 383, 422, 463, 506, 551, 598, 647, 698, 751, 806, 863, 922, 983, 1046, 1111, 1178, 1247, 1318, 1391, 1466, 1543, 1622, 1703, 1786, 1871, 1958, 2047, 2138, 2231, 2326, 2423

Offset

0,1

Comments

Old name was: "Numbers of the form x^2 + 22".

x^2 + 22 != y^n for all x,y and n > 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4 (1993).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(22 - 43*x + 23*x^2)/(1 - x)^3. - Vincenzo Librandi, Apr 30 2014

From Amiram Eldar, Nov 04 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(22)*Pi*coth(sqrt(22)*Pi))/44.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(22)*Pi*cosech(sqrt(22)*Pi))/44. (End)

Mathematica

Table[n^2 + 22, {n, 0, 60}] (* Vincenzo Librandi, Apr 30 2014 *)

Prog

(PARI) a(n)=n^2+22 \\ Amiram Eldar, Nov 04 2020
(Magma) [n^2+22: n in [0..60]]; // Vincenzo Librandi, Apr 30 2014

Crossrefs

Cf. similar sequences listed in A114962.

Sequence in context: A276182 A091404 A260994 * A146755 A106556 A106554

Adjacent sequences: A114960 A114961 A114962 * A114964 A114965 A114966

Keyword

nonn,easy

Author

Cino Hilliard, Feb 21 2006

Extensions

a(0)=22 from Vincenzo Librandi, Apr 30 2014

Definition changed by Bruno Berselli, Mar 13 2015

Offset corrected by Amiram Eldar, Nov 04 2020

Status

approved