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A267984 Numbers congruent to {17, 23} mod 30. 3
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 (list; graph; refs; listen; history; text; internal format)
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)

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

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Last modified April 4 21:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)