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

Author

Bruno Berselli, May 24 2016

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A001014, A016746, A017322, A017346

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

Programs

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]];

Mathematica

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

Maxima

makelist((10*n-3*(-1)^n-5)^6/64, n, 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)]

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.