A298360 Numbers congruent to {3, 7, 13, 27} mod 30.
3, 7, 13, 27, 33, 37, 43, 57, 63, 67, 73, 87, 93, 97, 103, 117, 123, 127, 133, 147, 153, 157, 163, 177, 183, 187, 193, 207, 213, 217, 223, 237, 243, 247, 253, 267, 273, 277, 283, 297, 303, 307, 313, 327, 333, 337, 343, 357, 363, 367, 373, 387, 393, 397, 403
Offset: 1
Examples
37 belongs to this sequence and d = 37*2^16 + 1 is a divisor of F(9) = 2^(2^9) + 1, so 10 | (37 + (F(9)/d - 1)/2^16).
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Wikipedia, Fermat number
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
-
Magma
[n: n in [0..403] | n mod 30 in {3, 7, 13, 27}]; -
Mathematica
LinearRecurrence[{1, 0, 0, 1, -1}, {3, 7, 13, 27, 33}, 60] CoefficientList[ Series[(3 + 4x + 6x^2 + 14x^3 + 3x^4)/((-1 + x)^2 (1 + x + x^2 + x^3)), {x, 0, 54}], x] (* Robert G. Wilson v, Feb 08 2018 *) Select[Range[500],MemberQ[{3,7,13,27},Mod[#,30]]&] (* Harvey P. Dale, Nov 15 2024 *) -
PARI
Vec(x*(3 + 4*x + 6*x^2 + 14*x^3 + 3*x^4)/((1 + x)*(1 + x^2)*(1 - x)^2 + O(x^55)))
Formula
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
a(n) = a(n-4) + 30.
G.f.: x*(3 + 4*x + 6*x^2 + 14*x^3 + 3*x^4)/((1 + x)*(1 + x^2)*(1 - x)^2).
Comments