A306278 Numbers congruent to 2 or 11 mod 14.

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

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