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A267985 Numbers congruent to {7, 13} mod 30. 4
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 (list; graph; refs; listen; history; text; internal format)
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)

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 A155036 A088985

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

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Last modified August 3 03:52 EDT 2021. Contains 346435 sequences. (Running on oeis4.)