This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269100 #56 May 31 2024 05:48:03
%S A269100 11,24,37,50,63,76,89,102,115,128,141,154,167,180,193,206,219,232,245,
%T A269100 258,271,284,297,310,323,336,349,362,375,388,401,414,427,440,453,466,
%U A269100 479,492,505,518,531,544,557,570,583,596,609,622,635,648,661,674,687,700,713,726,739
%N A269100 a(n) = 13*n + 11.
%C A269100 Any square mod 13 is one of 0, 1, 3, 4, 9, 10 or 12 (A010376) but not 11, and for this reason there are no squares in the sequence. Likewise, any cube mod 13 is one of 0, 1, 5, 8 or 12, therefore no a(k) is a cube.
%C A269100 Sequences of the type 13*n + k, for k = 0..12, without squares and cubes:
%C A269100 k = 2: A153080,
%C A269100 k = 6: A186113,
%C A269100 k = 7: A269044,
%C A269100 k = 11: this case.
%C A269100 The sum of the sixth powers of any two terms of the sequence is also a term of the sequence. Example: a(3)^6 + a(8)^6 = a(179129674278) = 2328685765625.
%C A269100 The primes of the sequence are listed in A140373.
%H A269100 Bruno Berselli, <a href="/A269100/b269100.txt">Table of n, a(n) for n = 0..1000</a>
%H A269100 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A269100 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A269100 G.f.: (11 + 2*x)/(1 - x)^2.
%F A269100 a(n) = -A153080(-n-1).
%F A269100 Sum_{i = h..h+13*k} a(i) = a(h*(13*k + 1) + k*(169*k + 35)/2).
%F A269100 Sum_{i >= 0} 1/a(i)^2 = .012486605016510955990... = polygamma(1, 11/13)/13^2.
%F A269100 E.g.f.: (11 + 13*x)*exp(x). - _G. C. Greubel_, May 31 2024
%t A269100 13 Range[0,60] + 11
%t A269100 Range[11, 800, 13]
%t A269100 Table[13 n + 11, {n, 0, 60}] (* _Bruno Berselli_, Feb 22 2016 *)
%t A269100 LinearRecurrence[{2,-1},{11,24},60] (* _Harvey P. Dale_, Jun 14 2023 *)
%o A269100 (PARI) vector(60, n, n--; 13*n+11)
%o A269100 (Sage) [13*n+11 for n in range(61)]
%o A269100 (Python) [13*n+11 for n in range(61)]
%o A269100 (Maxima) makelist(13*n+11, n, 0, 60);
%o A269100 (Magma) [13*n+11: n in [0..60]];
%Y A269100 Subsequence of A094784, A106389.
%Y A269100 Cf. A140373.
%Y A269100 Similar sequences of the type k*n+k-2: A023443 (k=1), A005843 (k=2), A016777 (k=3), A016825 (k=4), A016885 (k=5), A016957 (k=6), A017041 (k=7), A017137 (k=8), A017245 (k=9), A017365 (k=10), A017497 (k=11), A017641 (k=12).
%Y A269100 Sequences of the form 13*n+q: A008595 (q=0), A190991 (q=1), A153080 (q=2), A127547 (q=4), A154609 (q=5), A186113 (q=6), A269044 (q=7), this sequence (q=11).
%K A269100 nonn,easy
%O A269100 0,1
%A A269100 _Bruno Berselli_, Feb 19 2016