A267985 Numbers congruent to {7, 13} mod 30.

7, 13, 37, 43, 67, 73, 97, 103, 127, 133, 157, 163, 187, 193, 217, 223, 247, 253, 277, 283, 307, 313, 337, 343, 367, 373, 397, 403, 427, 433, 457, 463, 487, 493, 517, 523, 547, 553, 577, 583, 607, 613, 637, 643, 667, 673, 697, 703, 727, 733, 757, 763

Offset

1,1

Comments

Union of A128471 and A082369.

For all k >= 1 the numbers 2^k - a(n) and a(n)*2^k - 1 do not form a pair of primes, where n is any positive integer.

Links

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

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

Formula

a(n) = a(n-1) + a(n-2) - a(n-3), n >= 4.

G.f.: x*(7 + 6*x + 17*x^2)/((1 + x)*(1 - x)^2).

a(n) = a(n-2) + 30.

a(n) = 10*(3*n - 4) - a(n-1).

From Colin Barker, Jan 24 2016: (Start)

a(n) = (30*n-9*(-1)^n-25)/2 for n>0.

a(n) = 15*n-17 for n>0 and even.

a(n) = 15*n-8 for n odd.

(End)

E.g.f.: 17 + ((30*x - 25)*exp(x) - 9*exp(-x))/2. - David Lovler, Sep 10 2022

Mathematica

LinearRecurrence[{1, 1, -1}, {7, 13, 37}, 52]

Prog

(Magma) [n: n in [0..763] | n mod 30 in {7, 13}];
(PARI) Vec(x*(7 + 6*x + 17*x^2)/((1 + x)*(1 - x)^2) + O(x^53))

Crossrefs

Cf. A082369, A128471, A267984.

Sequence in context: A066673 A307762 A290947 * A173230 A361483 A155036

Adjacent sequences: A267982 A267983 A267984 * A267986 A267987 A267988

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Jan 23 2016

Extensions

Comment corrected by Philippe Deléham, Nov 28 2016

Status

approved