|
| |
|
|
A227863
|
|
Numbers congruent to {1,49} mod 120.
|
|
1
|
|
|
|
1, 49, 121, 169, 241, 289, 361, 409, 481, 529, 601, 649, 721, 769, 841, 889, 961, 1009, 1081, 1129, 1201, 1249, 1321, 1369, 1441, 1489, 1561, 1609, 1681, 1729, 1801, 1849, 1921, 1969, 2041, 2089, 2161, 2209, 2281, 2329, 2401, 2449, 2521, 2569, 2641, 2689
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The squares of natural numbers not divisible by 2, 3 or 5 and therefore the squares of prime numbers >5 are confined to this sequence.
|
|
|
LINKS
|
Bruno Berselli, Table of n, a(n) for n = 1..1000
Gary W. Croft Twin Primes Demystified
Gary W. Croft Matrix Demonstrating Distribution of Squares Congruent to {1,49} mod 120
Gary W. Croft Matrix: square roots of squares congruent to {1,49} mod 120
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
|
|
|
FORMULA
|
G.f.: x*(1 + 48*x + 71*x^2)/((1 + x)*(1 - x)^2). [Bruno Berselli, Nov 04 2013]
a(n) = 60*n - 6*(-1)^n - 65. [Bruno Berselli, Nov 04 2013]
|
|
|
MATHEMATICA
|
Table[60 n - 6 (-1)^n - 65, {n, 50}] (* Bruno Berselli, Nov 04 2013 *)
|
|
|
PROG
|
(PARI) a(n)=n\2*120+[-71, 1][n%2+1] \\ Charles R Greathouse IV, Aug 26 2014
|
|
|
CROSSREFS
|
Cf. A000040, A001248, A007775.
Sequence in context: A163245 A084733 A338499 * A339131 A115557 A167718
Adjacent sequences: A227860 A227861 A227862 * A227864 A227865 A227866
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Gary Croft, Nov 01 2013
|
|
|
STATUS
|
approved
|
| |
|
|
