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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

COMMENTS

Conjecture: A306289(n) = A007310(m + 1) when n is congruent to {m, A306277(m + 1)} (mod A091999(m + 1)) but not congruent to {k, A306277(k + 1)} (mod A091999(k + 1)), m > k >= 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

MAPLE

seq(seq(14*i+j, j=[2, 11]), i=0..28);

MATHEMATICA

Flatten[Table[{14n + 2, 14n + 11}, {n, 0, 28}]]

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 April 5 11:18 EDT 2020. Contains 333239 sequences. (Running on oeis4.)