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 A186113 #50 May 31 2024 05:17:48
%S A186113 6,19,32,45,58,71,84,97,110,123,136,149,162,175,188,201,214,227,240,
%T A186113 253,266,279,292,305,318,331,344,357,370,383,396,409,422,435,448,461,
%U A186113 474,487,500,513,526,539,552,565,578,591,604,617,630,643,656,669,682
%N A186113 a(n) = 13*n + 6.
%C A186113 These numbers appear in the G. E. Andrews paper, for example: see the abstract, formula (1.7), etc. Also "13n + 6" appears in the Folsom-Ono paper (see links).
%C A186113 Row 6 of triangle A151890 lists the first seven terms of this sequence.
%C A186113 Any square mod 13 is one of 0, 1, 3, 4, 9, 10 or 12 (A010376) but not 6, 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. - _Bruno Berselli_, Feb 19 2016
%H A186113 G. C. Greubel, <a href="/A186113/b186113.txt">Table of n, a(n) for n = 0..5000</a>
%H A186113 G. E. Andrews, <a href="http://www.math.psu.edu/vstein/alg/antheory/preprint/andrews/17.pdf">The number of smallest parts in the partitions of n</a>, <a href="http://dx.doi.org/10.1515/CRELLE.2008.083">J. Reine Angew. Math. 624 (2008) 133</a>
%H A186113 Amanda Folsom and Ken Ono, <a href="https://doi.org/10.1073/pnas.0809431105">The spt-function of Andrews</a>, Proc. Natl. Acad. Sci. USA 105 (51) (2008) 20152-20156.
%H A186113 Ken Ono, <a href="https://doi.org/10.1073/pnas.1015339107">Congruences for the Andrews spt-function</a>, Proc. Natl. Acad. Sci. USA 108 (2011) 473-476.
%H A186113 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A186113 G.f.: (6+7*x)/(1-x)^2.
%F A186113 E.g.f.: (6 + 13*x)*exp(x). - _G. C. Greubel_, May 31 2024
%t A186113 Range[6, 1000, 13] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)
%t A186113 LinearRecurrence[{2,-1},{6,19},60] (* _Harvey P. Dale_, May 12 2023 *)
%o A186113 (Magma) [13*n+6: n in [0..60]]; // _G. C. Greubel_, May 31 2024
%o A186113 (SageMath) [13*n+6 for n in range(61)] # _G. C. Greubel_, May 31 2024
%Y A186113 Cf. A092269, A151890.
%Y A186113 Sequences of the form 13*n+q: A008595 (q=0), A190991 (q=1), A153080 (q=2),
%Y A186113 A127547 (q=4), A154609 (q=5), this sequence (q=6), A269044 (q=7), A269100 (q=11).
%K A186113 nonn,easy
%O A186113 0,1
%A A186113 _Omar E. Pol_, Feb 12 2011