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 A271346 #30 Sep 08 2022 08:46:16
%S A271346 4,6,8,12,14,16,24,26,28,32,34,36,44,46,48,52,54,56,64,66,68,72,74,76,
%T A271346 84,86,88,92,94,96,104,106,108,112,114,116,124,126,128,132,134,136,
%U A271346 144,146,148,152,154,156,164,166,168,172,174,176,184,186,188,192,194
%N A271346 Numbers k such that the final digit of k^k is 6.
%C A271346 The values of n^n (A000312) end in every digit except for 2 and 8. The sequence of final digits of n^n (A056849) is periodic with period 20; for n=1,2,... the last digits are [1, 4, 7, 6, 5, 6, 3, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 4, 9, 0]. Thus, 6 is the most common final digit of n^n. Since 6 does not occur at any odd index in the list above, all terms of a(n) are even. Also, from the distribution of 6's in the list, we can see that the difference between any two consecutive values of a(n) will be 2, 4 or 8.
%H A271346 Felix Fröhlich, <a href="/A271346/b271346.txt">Table of n, a(n) for n = 1..10000</a>
%H A271346 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A271346 a(n) = a(n-1) + a(n-6) - a(n-7) for n > 7. - _Wesley Ivan Hurt_, Oct 08 2017
%F A271346 G.f.: 2*x*(1 + x^2)*(2 + x - x^2 + x^3 + 2*x^4) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)). - _Colin Barker_, Dec 13 2018
%p A271346 A271346:=n->`if`(n^n mod 10 = 6, n, NULL): seq(A271346(n), n=1..500);
%t A271346 LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {4, 6, 8, 12, 14, 16, 24},59] (* _Ray Chandler_, Mar 08 2017 *)
%o A271346 (PARI) is(n) = Mod(n, 10)^n==6 \\ _Felix Fröhlich_, Apr 07 2016
%o A271346 (Magma) I:=[4,6,8,12,14,16,24]; [n le 7 select I[n] else Self(n-1)+Self(n-6)-Self(n-7): n in [1..60]]; // _Vincenzo Librandi_, Oct 09 2017
%o A271346 (PARI) Vec(2*x*(1 + x^2)*(2 + x - x^2 + x^3 + 2*x^4) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)) + O(x^59)) \\ _Colin Barker_, Dec 13 2018
%Y A271346 Cf. A000312 (n^n), A056849 (final digit of n^n).
%K A271346 nonn,base,easy
%O A271346 1,1
%A A271346 _Wesley Ivan Hurt_, Apr 04 2016