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A272914 Sixth powers ending in digit 6.

%I A272914 #18 Sep 08 2022 08:46:16
%S A272914 4096,46656,7529536,16777216,191102976,308915776,1544804416,
%T A272914 2176782336,7256313856,9474296896,24794911296,30840979456,68719476736,
%U A272914 82653950016,164206490176,192699928576,351298031616,404567235136,689869781056,782757789696,1265319018496,1418519112256,2194972623936
%N A272914 Sixth powers ending in digit 6.
%C A272914 Other sequences of k-th powers ending in digit k are: A017281 (k=1), A017355 (k=3), A017333 (k=5), A017311 (k=7), A017385 (k=9). It is missing k=4 because the fourth powers end with 0, 1, 5 or 6.
%C A272914 Union of A017322 and A017346.
%C A272914 a(h)^(1/6) is a member of A068408 for h = 2, 4, 8, 12, 16, 20, 36, 76, ...
%H A272914 Bruno Berselli, <a href="/A272914/b272914.txt">Table of n, a(n) for n = 1..1000</a>
%H A272914 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
%F A272914 O.g.f.: 64*x*(64 + 665*x + 116536*x^2 + 140505*x^3 + 2023280*x^4 + 983830*x^5 + 4720240*x^6 + 983830*x^7 + 2023280*x^8 + 140505*x^9 + 116536*x^10 + 665*x^11 + 64*x^12)/((1 + x)^6*(1 - x)^7).
%F A272914 E.g.f.: (-8192 + 45*(91 + 182*x - 5250*x^2 + 16000*x^3 - 9375*x^4 + 1250*x^5)*exp(-x) + (4097 + 287000*x^2 + 1262500*x^3 + 1253125*x^4 + 375000*x^5 + 31250*x^6)*exp(x))/2.
%F A272914 a(n) = (10*n - 3*(-1)^n - 5)^6/64 = 64*A047221(n)^6.
%t A272914 Table[(10 n - 3 (-1)^n - 5)^6/64, {n, 1, 30}]
%o A272914 (Magma) /* By definition: */ k:=6; [n^k: n in [0..200] | Modexp(n, k, 10) eq k];
%o A272914 (Magma) [(10*n-3*(-1)^n-5)^6/64: n in [1..30]];
%o A272914 (PARI) vector(30, n, nn; (10*n-3*(-1)^n-5)^6/64)
%o A272914 (Sage) [(10*n-3*(-1)^n-5)^6/64 for n in (1..30)]
%o A272914 (Maxima) makelist((10*n-3*(-1)^n-5)^6/64, n, 1, 30);
%Y A272914 Cf. A001014, A016746, A017322, A017346
%Y A272914 Similar sequences (see comment): A017281, A017311, A017333, A017355, A017385.
%K A272914 nonn,base,easy
%O A272914 1,1
%A A272914 _Bruno Berselli_, May 24 2016