A272914 - OEIS

%I #18 Sep 08 2022 08:46:16

%S 4096,46656,7529536,16777216,191102976,308915776,1544804416,

%T 2176782336,7256313856,9474296896,24794911296,30840979456,68719476736,

%U 82653950016,164206490176,192699928576,351298031616,404567235136,689869781056,782757789696,1265319018496,1418519112256,2194972623936

%N Sixth powers ending in digit 6.

%C 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 Union of A017322 and A017346.

%C a(h)^(1/6) is a member of A068408 for h = 2, 4, 8, 12, 16, 20, 36, 76, ...

%H Bruno Berselli, <a href="/A272914/b272914.txt">Table of n, a(n) for n = 1..1000</a>

%H <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 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 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 a(n) = (10*n - 3*(-1)^n - 5)^6/64 = 64*A047221(n)^6.

%t Table[(10 n - 3 (-1)^n - 5)^6/64, {n, 1, 30}]

%o (Magma) /* By definition: */ k:=6; [n^k: n in [0..200] | Modexp(n, k, 10) eq k];

%o (Magma) [(10*n-3*(-1)^n-5)^6/64: n in [1..30]];

%o (PARI) vector(30, n, nn; (10*n-3*(-1)^n-5)^6/64)

%o (Sage) [(10*n-3*(-1)^n-5)^6/64 for n in (1..30)]

%o (Maxima) makelist((10*n-3*(-1)^n-5)^6/64, n, 1, 30);

%Y Cf. A001014, A016746, A017322, A017346

%Y Similar sequences (see comment): A017281, A017311, A017333, A017355, A017385.

%K nonn,base,easy

%O 1,1

%A _Bruno Berselli_, May 24 2016