A296716 Numbers congruent to {7, 11, 13, 29} mod 30.

7, 11, 13, 29, 37, 41, 43, 59, 67, 71, 73, 89, 97, 101, 103, 119, 127, 131, 133, 149, 157, 161, 163, 179, 187, 191, 193, 209, 217, 221, 223, 239, 247, 251, 253, 269, 277, 281, 283, 299, 307, 311, 313, 329, 337, 341, 343, 359, 367, 371, 373, 389, 397, 401, 403

Offset

1,1

Comments

For any m >= 0, if F(m) = 2^(2^m) + 1 has a factor of the form b = a(n)*2^k + 1 with k >= m + 2 and n >= 1, then the integer F(m)/b is congruent to 13 or 19 mod 30.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = a(n-1) + a(n-4) - a(n-5), n >= 6.

a(n) = a(n-4) + 30.

G.f.: x*(7 + 4*x + 2*x^2 + 16*x^3 + x^4)/((1 + x)*(1 + x^2)*(1 - x)^2).

a(n) = (-15 + 5*(-1)^n + (3+9*i)*(-i)^n + (3-9*i)*i^n + 30*n) / 4 where i=sqrt(-1). - Colin Barker, Dec 19 2017

E.g.f.: (5*(e^(-x) + (6*x - 3)*e^x) + 6*cos(x) + 18*sin(x))/4. - Iain Fox, Dec 19 2017

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {7, 11, 13, 29, 37}, 60]

Prog

(Magma) [n: n in [0..403] | n mod 30 in {7, 11, 13, 29}];
(PARI) Vec(x*(7 + 4*x + 2*x^2 + 16*x^3 + x^4)/((1 + x)*(1 + x^2)*(1 - x)^2 + O(x^55)))

Crossrefs

Cf. A191062, A267985.

Sequence in context: A155760 A058500 A090865 * A191062 A106079 A235478

Adjacent sequences: A296713 A296714 A296715 * A296717 A296718 A296719

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Dec 19 2017

Status

approved