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A047382 Numbers that are congruent to {0, 5} mod 7. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..49.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = 7*n - a(n-1) - 9 for n>1, with a(1)=0. - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=5 and b(k)=A005009(k-1)=7*2^(k-1) for k>0. - Philippe Deléham, Oct 17 2011

From Bruno Berselli, Oct 17 2011:  (Start)

G.f.: x^2*(5 + 2*x)/((1 + x)*(1 - x)^2).

a(n) = (14*n + 3*(-1)^n - 11)/4.

a(-n) = -A047352(n+2). (End)

a(n) = ceiling((7/3)*ceiling(3*n/2)). - Clark Kimberling, Jul 04 2012

MATHEMATICA

{#, 5 + #} &/@ (7 Range[0, 30]) // Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 5, 7}, 60] (* Harvey P. Dale, Dec 01 2016 *)

PROG

(MAGMA) &cat[[7*n, 7*n+5]: n in [0..23]];  // Bruno Berselli, Oct 17 2011

CROSSREFS

Cf. A008589, A017041.

Sequence in context: A306513 A286901 A171490 * A314301 A314302 A314303

Adjacent sequences:  A047379 A047380 A047381 * A047383 A047384 A047385

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 16 16:32 EST 2022. Contains 350376 sequences. (Running on oeis4.)