A272914 - OEIS

A272914

Sixth powers ending in digit 6.

4096, 46656, 7529536, 16777216, 191102976, 308915776, 1544804416, 2176782336, 7256313856, 9474296896, 24794911296, 30840979456, 68719476736, 82653950016, 164206490176, 192699928576, 351298031616, 404567235136, 689869781056, 782757789696, 1265319018496, 1418519112256, 2194972623936

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OFFSET

1,1

COMMENTS

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.

Union of A017322 and A017346.

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

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

FORMULA

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).

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.

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

MATHEMATICA

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

PROG

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

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

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

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

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

CROSSREFS

Cf. A001014, A016746, A017322, A017346

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