|
|
A051062
|
|
a(n) = 16*n + 8.
|
|
15
|
|
|
8, 24, 40, 56, 72, 88, 104, 120, 136, 152, 168, 184, 200, 216, 232, 248, 264, 280, 296, 312, 328, 344, 360, 376, 392, 408, 424, 440, 456, 472, 488, 504, 520, 536, 552, 568, 584, 600, 616, 632, 648, 664, 680, 696, 712, 728, 744, 760, 776, 792, 808, 824, 840
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0(97).
n such that 32 is the largest power of 2 dividing A003629(k)^n-1 for any k. - Benoit Cloitre, Mar 23 2002
Continued fraction expansion of tanh(1/8). - Benoit Cloitre, Dec 17 2002
If Y and Z are 2-blocks of a (4n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 28 2007
a(n)*n+1 = (4n+1)^2 and a(n)*(n+1)+1 = (4n+3)^2 are both perfect squares. - Carmine Suriano, Jun 01 2014
For all positive integers n, there are infinitely many positive integers k such that k*n + 1 and k*(n+1) + 1 are both perfect squares. Except for 8, all the numbers of this sequence are the smallest integers k which are solutions for getting two perfect squares. Example: a(1) = 24 and 24 * 1 + 1 = 25 = 5^2, then 24 * (1+1) + 1 = 49 = 7^2. [Reference AMM] - Bernard Schott, Sep 24 2017
Numbers k such that 3^k + 1 is divisible by 17*193. - Bruno Berselli, Aug 22 2018
|
|
REFERENCES
|
Letter from Gary W. Adamson concerning Prouhet-Thue-Morse sequence, Nov 11 1999
|
|
LINKS
|
Mihaly Bencze, Problem 11508, The American Mathematical Monthly, Vol. 117, N° 5, May 2010, p. 459.
|
|
FORMULA
|
|
|
MAPLE
|
|
|
MATHEMATICA
|
LinearRecurrence[{2, -1}, {8, 24}, 60] (* or *) NestList[#+16&, 8, 60] (* Harvey P. Dale, Aug 18 2019 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|