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A047621 Numbers that are congruent to {3, 5} mod 8. 16
3, 5, 11, 13, 19, 21, 27, 29, 35, 37, 43, 45, 51, 53, 59, 61, 67, 69, 75, 77, 83, 85, 91, 93, 99, 101, 107, 109, 115, 117, 123, 125, 131, 133, 139, 141, 147, 149, 155, 157, 163, 165, 171, 173, 179, 181, 187, 189, 195, 197, 203, 205, 211, 213, 219, 221, 227, 229 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd numbers n such that x^2 == 2 (mod n) has no solution, i.e., those n for which Jacobi symbol J(2,n) = -1. - Antti Karttunen, Aug 27 2005

Hence also odd numbers n such that 2^n is not a square mod n.

A089911(3*a(n)) = 10. - Reinhard Zumkeller, Jul 05 2013

Numbers n whose multiplicative order modulo 2^k is 2^(k - 2) for k >= 4. For k = 3, the numbers whose multiplicative order modulo 8 is 2 are in sequence A047484. - Jianing Song, Apr 29 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..5000

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

FORMULA

a(n) = 8*n - a(n-1) - 8 (with a(1) = 3). - Vincenzo Librandi, Aug 06 2010

G.f.: x*(3 + 2*x + 3*x^2) / ( (1 + x)*(x - 1)^2 ). - R. J. Mathar, Oct 08 2011

a(n) = 8*floor((n - 1)/2) + 4 + (-1)^n. - Gary Detlefs, Dec 03 2018

From Franck Maminirina Ramaharo, Dec 03 2018: (Start)

a(n) = 4*n - 2 - (-1)^n.

E.g.f.: 3 - (2 - 4*x)*exp(x) - exp(-x). (End)

a(n + 2) = a(n) + 8. - David A. Corneth, Dec 03 2018

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {3, 5, 11}, 100] (* Jean-Fran├žois Alcover, Jul 31 2018 *)

PROG

(Haskell)

a047621 n = a047621_list !! (n-1)

a047621_list = 3 : 5 : map (+ 8) a047621_list

-- Reinhard Zumkeller, Jul 05 2013

(GAP) a:=[3];; for n in [2..60] do a[n]:=8*n-a[n-1]-8; od; a; # Muniru A Asiru, Dec 04 2018

CROSSREFS

Row 1 of A112070. Complement of A047522 relative to A005408. Primes in this sequence: A003629.

Cf. A066507.

Cf. A047522.

Sequence in context: A153443 A211876 A066587 * A239636 A117205 A147992

Adjacent sequences:  A047618 A047619 A047620 * A047622 A047623 A047624

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)