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A047382
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Numbers that are congruent to {0, 5} mod 7.
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5
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0, 5, 7, 12, 14, 19, 21, 26, 28, 33, 35, 40, 42, 47, 49, 54, 56, 61, 63, 68, 70, 75, 77, 82, 84, 89, 91, 96, 98, 103, 105, 110, 112, 117, 119, 124, 126, 131, 133, 138, 140, 145, 147, 152, 154, 159, 161, 166, 168
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OFFSET
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1,2
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COMMENTS
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Except for the first term, numbers m such that 36*m^2 + 72*m + 35 = (6*m+5)*(6*m+7) is not of the form p*(p+2), with p prime. - Vincenzo Librandi, Aug 05 2010
Nonnegative k such that k or 4*k + 1 is divisible by 7. - Bruno Berselli, Feb 13 2018
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LINKS
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FORMULA
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G.f.: x^2*(5 + 2*x)/((1 + x)*(1 - x)^2).
a(n) = (14*n + 3*(-1)^n - 11)/4.
E.g.f.: 2 + ((14*x - 11)*exp(x) + 3*exp(-x))/4. - David Lovler, Sep 11 2022
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MATHEMATICA
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{#, 5 + #} &/@ (7 Range[0, 30]) // Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 5, 7}, 60] (* Harvey P. Dale, Dec 01 2016 *)
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PROG
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(Magma) &cat[[7*n, 7*n+5]: n in [0..23]]; // Bruno Berselli, Oct 17 2011
(PARI) a(n) = (14*n + 3*(-1)^n - 11)/4 \\ David Lovler, Sep 11 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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