A017413 -id:A017413 - cp's OEIS frontend

A017509 a(n) = 11*n + 10.

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 362, 373, 384, 395, 406, 417, 428, 439, 450, 461, 472, 483, 494, 505, 516, 527, 538, 549, 560, 571, 582

Offset: 0

N. J. A. Sloane

If k is any member of A045572, the sequence lists the numbers n such that (n^k+1)/11 is a nonnegative integer. See also A267541. - Bruno Berselli, Jan 16 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 989
Leo Tavares, Illustration: Triangular Lines
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017413, A045572, A267541.
Cf. A211013 (partial sums), A254322 (partial products).
Powers of the form (11*n+10)^m: this sequence (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).
Cf. A008591, A005408.

List([0..60], n-> (11*n+10)); # G. C. Greubel, Oct 29 2019

[11*n+10: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

seq((11*n+10), n=0..60); # G. C. Greubel, Oct 29 2019

Range[10, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
(11*Range[60] -1) (* G. C. Greubel, Oct 29 2019 *)

a(n)=11*n+10 \\ Charles R Greathouse IV, Jul 10 2016

def a(n): return 11*n + 10
print([a(n) for n in range(53)]) # Michael S. Branicky, Oct 21 2021

[(11*n+10) for n in (0..60)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (10 + x)/(1-x)^2.
E.g.f.: (10 + 11*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2). (End)
a(n) = A008591(n+1) + A005408(n). - Leo Tavares, Oct 25 2022

A017473 a(n) = 11*n + 7.

Original entry on oeis.org

7, 18, 29, 40, 51, 62, 73, 84, 95, 106, 117, 128, 139, 150, 161, 172, 183, 194, 205, 216, 227, 238, 249, 260, 271, 282, 293, 304, 315, 326, 337, 348, 359, 370, 381, 392, 403, 414, 425, 436, 447, 458, 469, 480, 491, 502, 513, 524, 535, 546, 557, 568, 579, 590

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017413.

Powers of the form (11*n+7)^m: this sequence (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..60], n-> 11*n+7); # G. C. Greubel, Sep 19 2019

[(11*n+7): n in [0..60]]; // Vincenzo Librandi, Sep 04 2011

seq(11*n+7, n=0..60); # G. C. Greubel, Sep 19 2019

Range[7, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)

vector(60, n, 11*n-4) \\ G. C. Greubel, Sep 19 2019

[11*n+7 for n in (0..60)] # G. C. Greubel, Sep 19 2019

From Colin Barker, Jun 06 2012: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (7 + 4*x)/(1-x)^2. (End)
E.g.f.: (7 + 11*x)*exp(x). - G. C. Greubel, Sep 19 2019

A017497 a(n) = 11*n + 9.

Original entry on oeis.org

9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 119, 130, 141, 152, 163, 174, 185, 196, 207, 218, 229, 240, 251, 262, 273, 284, 295, 306, 317, 328, 339, 350, 361, 372, 383, 394, 405, 416, 427, 438, 449, 460, 471, 482, 493, 504, 515, 526, 537, 548, 559, 570, 581, 592

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017413.

Powers of the form (11*n+9)^m: this sequence (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

List([0..60], n-> 11*n+9); # G. C. Greubel, Oct 28 2019

[11*n+9: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

seq(11*n+9, n=0..60); # G. C. Greubel, Oct 28 2019

Range[9, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
(11*Range[60] - 2) (* G. C. Greubel, Oct 28 2019 *)

a(n)=11*n+9 \\ Charles R Greathouse IV, Jul 10 2016

[11*n+9 for n in (0..60)] # G. C. Greubel, Oct 28 2019

From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (9+2*x)/(1-x)^2.
E.g.f.: (9+11*x)*exp(x). (End)

A017401 a(n) = 11n + 1.

Original entry on oeis.org

1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 210, 221, 232, 243, 254, 265, 276, 287, 298, 309, 320, 331, 342, 353, 364, 375, 386, 397, 408, 419, 430, 441, 452, 463, 474, 485, 496, 507, 518, 529, 540, 551, 562, 573, 584, 595, 606, 617, 628, 639, 650, 661

Offset: 0

N. J. A. Sloane

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=11, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=2, a(n-1)=-charpoly(A,x^(n-1)). - Milan Janjic, Feb 21 2010

Sequence lists all nonnegative solutions to x^k == 1 (mod 11), where k is a member of A045572. - Bruno Berselli, Jan 18 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017281, A017413.

[11*n+1: n in [0..60]]; // Vincenzo Librandi, Jul 30 2011

Range[1, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)

a(n)=11*n+1 \\ Charles R Greathouse IV, Jan 18 2016

G.f.: (1+10*x)/(1-x)^2.

E.g.f.: exp(x)*(1 + 11*x). - Stefano Spezia, Oct 08 2022

A017425 a(n) = 11*n + 3.

Original entry on oeis.org

3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 124, 135, 146, 157, 168, 179, 190, 201, 212, 223, 234, 245, 256, 267, 278, 289, 300, 311, 322, 333, 344, 355, 366, 377, 388, 399, 410, 421, 432, 443, 454, 465, 476, 487, 498, 509, 520, 531, 542, 553, 564, 575, 586

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017413, A226492.

[11*n+3: n in [0..60]]; // Vincenzo Librandi, Sep 02 2011

11Range[0,50]+3  (* Harvey P. Dale, Apr 21 2011 *)

a(n)=11*n+3 \\ Charles R Greathouse IV, Jul 10 2016

[i+3 for i in range(475) if gcd(i,11) == 11] # Zerinvary Lajos, May 21 2009

From Elmo R. Oliveira, Apr 03 2024: (Start)
G.f.: (3+8*x)/(1-x)^2.
E.g.f.: exp(x)*(3 + 11*x).
a(n) = A226492(n+1) - A226492(n).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

Terms corrected by Vincenzo Librandi, Sep 02 2011

A139612 a(n) = 66*n + 12.

Original entry on oeis.org

12, 78, 144, 210, 276, 342, 408, 474, 540, 606, 672, 738, 804, 870, 936, 1002, 1068, 1134, 1200, 1266, 1332, 1398, 1464, 1530, 1596, 1662, 1728, 1794, 1860, 1926, 1992, 2058, 2124, 2190, 2256, 2322, 2388, 2454, 2520, 2586, 2652, 2718

Offset: 0

Omar E. Pol, Apr 27 2008

Numbers of the 12th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 12th column in the square array A057145.

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017413, A057145, A139600.

[6*(11*n + 2): n in [0..60]]; // Vincenzo Librandi, Jul 23 2011

66*Range[0,50]+12 (* or *) LinearRecurrence[{2,-1},{12,78},50] (* Harvey P. Dale, Jun 14 2017 *)

a(n)=66*n+12 \\ Charles R Greathouse IV, Oct 05 2011

From Elmo R. Oliveira, Apr 03 2024: (Start)
G.f.: 6*(2+9*x)/(x-1)^2.
E.g.f.: 6*exp(x)*(2 + 11*x).
a(n) = 6*A017413(n).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

A111312 Numbers n such that 11*n + 2 is prime.

Original entry on oeis.org

0, 1, 7, 9, 15, 19, 21, 25, 37, 39, 49, 51, 55, 61, 67, 69, 75, 85, 97, 99, 109, 111, 117, 127, 135, 139, 141, 145, 147, 151, 169, 177, 181, 189, 201, 217, 219, 225, 229, 231, 237, 247, 249, 259, 265, 267, 277, 285, 289, 291, 301, 315, 319, 321, 331, 337, 345

Offset: 1

Parthasarathy Nambi, Nov 03 2005

			If n=135 then 11*n + 2 = 1487 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A017413, A090187.

[n: n in [0..100000] |IsPrime(11*n + 2)] // Vincenzo Librandi, Nov 13 2010

Select[Range[0,400],PrimeQ[11#+2]&] (* Harvey P. Dale, Mar 22 2020 *)

is(n)=isprime(11*n+2) \\ Charles R Greathouse IV, Jun 13 2017

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A017509 a(n) = 11*n + 10.

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A017473 a(n) = 11*n + 7.

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A017497 a(n) = 11*n + 9.

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A017401 a(n) = 11n + 1.

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A017425 a(n) = 11*n + 3.

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A139612 a(n) = 66*n + 12.

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