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 A306278 Numbers congruent to 2 or 11 mod 14. 1
 2, 11, 16, 25, 30, 39, 44, 53, 58, 67, 72, 81, 86, 95, 100, 109, 114, 123, 128, 137, 142, 151, 156, 165, 170, 179, 184, 193, 198, 207, 212, 221, 226, 235, 240, 249, 254, 263, 268, 277, 282, 291, 296, 305, 310, 319, 324, 333, 338, 347, 352, 361, 366, 375, 380, 389, 394 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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) = 7*n - A010703(n). a(n) = 7*n - 4 + (-1)^n. a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3. A007310(a(n) + 1) = 7*A007310(n) From Jinyuan Wang, Feb 03 2019: (Start) For odd number k, a(k) = 7*k - 5. For even number k, a(k) = 7*k - 3. (End) G.f.: x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)). - Colin Barker, Mar 14 2019 E.g.f.: 3 + (7*x - 4)*exp(x) + exp(-x). - David Lovler, Sep 07 2022 MAPLE seq(seq(14*i+j, j=[2, 11]), i=0..28); MATHEMATICA Flatten[Table[{14n + 2, 14n + 11}, {n, 0, 28}]] LinearRecurrence[{1, 1, -1}, {2, 11, 16}, 60] (* Harvey P. Dale, Jan 16 2023 *) PROG (PARI) for(n=2, 394, if((n%14==2) || (n%14==11), print1(n, ", "))) (PARI) for(n=1, 57, print1(7*n-4+(-1)^n, ", ")) (PARI) for(n=1, 500, if(n%14==2, print1(n, ", ")); if(n%14==11, print1(n, ", "))) \\ Jinyuan Wang, Feb 03 2019 (PARI) Vec(x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Mar 14 2019 (PARI) upto(n) = forstep(i = 2, n, [9, 5], print1(i", ")) \\ David A. Corneth, Mar 27 2019 CROSSREFS Cf. A007310, A010703, A020639, A047470, A091999, A273669, A306277, A306289. Primes greater than 2 in this sequence: A045471. Sequence in context: A272883 A257283 A091211 * A199397 A012019 A012185 Adjacent sequences: A306275 A306276 A306277 * A306279 A306280 A306281 KEYWORD nonn,easy AUTHOR Davis Smith, Feb 02 2019 STATUS approved

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Last modified September 27 06:33 EDT 2023. Contains 365674 sequences. (Running on oeis4.)