A267984 Numbers congruent to {17, 23} mod 30.

17, 23, 47, 53, 77, 83, 107, 113, 137, 143, 167, 173, 197, 203, 227, 233, 257, 263, 287, 293, 317, 323, 347, 353, 377, 383, 407, 413, 437, 443, 467, 473, 497, 503, 527, 533, 557, 563, 587, 593, 617, 623, 647, 653, 677, 683, 707, 713, 737, 743, 767, 773

Offset

1,1

Comments

Union of A128468 and A128473.

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

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

a(n) = 10*(3*n - 2) - a(n-1).

From Colin Barker, Jan 24 2016: (Start)

a(n) = (30*n - 9*(-1)^n - 5)/2 for n>0.

a(n) = 15*n - 7 for n>0 and even.

a(n) = 15*n + 2 for n odd.

(End)

E.g.f.: 7 + ((30*x - 5)*exp(x) - 9*exp(-x))/2. - David Lovler, Sep 10 2022

Mathematica

LinearRecurrence[{1, 1, -1}, {17, 23, 47}, 52]

Prog

(Magma) [n: n in [0..773] | n mod 30 in {17, 23}];
(PARI) Vec(x*(17 + 6*x + 7*x^2)/((1 + x)*(1 - x)^2) + O(x^53))

Crossrefs

Cf. A128468, A128473, A267985.

Sequence in context: A102874 A086532 A159044 * A281533 A278436 A126329

Adjacent sequences: A267981 A267982 A267983 * A267985 A267986 A267987

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Jan 23 2016

Status

approved