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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
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.
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Comment corrected by Philippe Deléham, Nov 28 2016
STATUS
approved