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A001533 a(n) = (8n+1)*(8n+7). 3
7, 135, 391, 775, 1287, 1927, 2695, 3591, 4615, 5767, 7047, 8455, 9991, 11655, 13447, 15367, 17415, 19591, 21895, 24327, 26887, 29575, 32391, 35335, 38407, 41607, 44935, 48391, 51975, 55687, 59527, 63495, 67591, 71815, 76167, 80647, 85255, 89991, 94855 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Klaus Purath, Aug 18 2022: (Start)

This is A028560(8*n+1), and thus a(n) + 9 is a square. (See formulas.)

7 is the only prime number of this sequence in which all odd prime factors occur.

Each prime factor p appears exactly twice in any interval of p consecutive terms. If a(m) and a(n) are within such an interval containing p, then m + n == -1 (mod p). (End)

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 4*A001539(n) - 5.

a(n) = 128*n + a(n-1) with a(0)=7. - Vincenzo Librandi, Nov 12 2010

Sum_{n>=0} 1/a(n) = (Psi(7/8)-Psi(1/8))/48 = 0.1580099..., see A250129. - R. J. Mathar, May 30 2022 [ = (sqrt(2)+1)*Pi/48. - Amiram Eldar, Sep 08 2022]

From Klaus Purath, Aug 18 2022: (Start)

a(n) = A028560(8*n+1).

a(n) + 9 = ((a(n+1) - a(n-1))/32)^2 = A017113(n)^2.

a(2*n) = (a(n+1) - a(n-1))*n + 7. (End)

MATHEMATICA

a[n_] := (8 n + 1)*(8 n + 7); Array[a, 40, 0] (* Amiram Eldar, Sep 08 2022 *)

PROG

(PARI) a(n)=(8*n+1)*(8*n+7) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A001539, A017113, A028560, A250129.

Sequence in context: A317216 A119670 A003374 * A143181 A183478 A292395

Adjacent sequences:  A001530 A001531 A001532 * A001534 A001535 A001536

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 29 14:20 EDT 2022. Contains 357090 sequences. (Running on oeis4.)