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

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.

Sequence in context: A223334 A231945 A220766 * A016996 A218527 A017068

Adjacent sequences: A272911 A272912 A272913 * A272915 A272916 A272917

Keyword

nonn,base,easy

Author

Bruno Berselli, May 24 2016

Status

approved