cp's OEIS Frontend

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.

A105814 a(n) = n^2 + (n concatenated with n).

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%I A105814 #28 Jan 04 2025 19:12:51
%S A105814 12,26,42,60,80,102,126,152,180,1110,1232,1356,1482,1610,1740,1872,
%T A105814 2006,2142,2280,2420,2562,2706,2852,3000,3150,3302,3456,3612,3770,
%U A105814 3930,4092,4256,4422,4590,4760,4932,5106,5282,5460,5640,5822,6006,6192,6380,6570
%N A105814 a(n) = n^2 + (n concatenated with n).
%H A105814 Michael S. Branicky, <a href="/A105814/b105814.txt">Table of n, a(n) for n = 1..10000</a>
%F A105814 a(n) = n^2 + n*(1+10^(1+floor(log_10(n)))). - _Robert Israel_, Jul 30 2015
%F A105814 a(n) = n^2 + A020338(n). - _Michel Marcus_, Jul 31 2015
%e A105814 1 + 11 = 12, 4 + 22 = 26, 9 + 33 = 42, 16 + 44 = 60, ..., 100 + 1010 = 1110.
%p A105814 seq(n^2 + n*(1+10^(1+ilog10(n))),n=1..100); # _Robert Israel_, Jul 30 2015
%t A105814 f[n_] := Block[{id = IntegerDigits[n]}, n^2 + FromDigits[ Join[id, id]]]; Table[ f[n], {n, 45}] (* _Robert G. Wilson v_, May 10 2005 *)
%o A105814 (PARI) vector(50, n, n^2 + eval(Str(n,n))) \\ _Michel Marcus_, Jul 31 2015
%o A105814 (Magma) [Seqint(Intseq(n) cat Intseq(n))+n^2: n in [1..50]]; // _Vincenzo Librandi_, Jul 31 2015
%o A105814 (Magma) [n^2+n*(1+10^(1+Floor(Log(n)/Log(10)))): n in [1..50]]; // _Vincenzo Librandi_, Jul 31 2015
%o A105814 (Python)
%o A105814 def a(n): return n**2 + int(str(n)*2)
%o A105814 print([a(n) for n in range(1, 47)]) # _Michael S. Branicky_, Dec 26 2021
%Y A105814 Cf. A020338.
%K A105814 base,easy,nonn
%O A105814 1,1
%A A105814 _Eric Angelini_, May 05 2005
%E A105814 More terms from _Robert G. Wilson v_, May 10 2005