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A322490 Numbers k such that k^k ends with 7. 2
3, 17, 23, 37, 43, 57, 63, 77, 83, 97, 103, 117, 123, 137, 143, 157, 163, 177, 183, 197, 203, 217, 223, 237, 243, 257, 263, 277, 283, 297, 303, 317, 323, 337, 343, 357, 363, 377, 383, 397, 403, 417, 423, 437, 443, 457, 463, 477, 483, 497, 503, 517, 523, 537, 543, 557, 563 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, numbers k such that k and (7^h)^k end with the same digit, where h == 1 (mod 4).

Also, numbers k such that k and (3^h)^k end with the same digit, where h == 3 (mod 4).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

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

FORMULA

O.g.f.: x*(3 + 14*x + 3*x^2)/((1 + x)*(1 - x)^2).

E.g.f.: 3 + 2*exp(-x) + 5*(2*x - 1)*exp(x).

a(n) = -a(-n+1) = a(n-1) + a(n-2) - a(n-3).

a(n) = 10*n + 2*(-1)^n - 5. Therefore:

a(n) = 10*n - 7 for odd n;

a(n) = 10*n - 3 for even n.

a(n+2*k) = a(n) + 20*k.

MAPLE

select(n->n^n mod 10=7, [$1..563]); # Paolo P. Lava, Dec 18 2018

MATHEMATICA

Table[10 n + 2 (-1)^n - 5, {n, 1, 60}]

LinearRecurrence[{1, 1, -1}, {3, 17, 23}, 80] (* Harvey P. Dale, Sep 15 2019 *)

PROG

(Sage) [10*n+2*(-1)^n-5 for n in (1..70)]

(Maxima) makelist(10*n+2*(-1)^n-5, n, 1, 70);

(GAP) List([1..70], n -> 10*n+2*(-1)^n-5);

(MAGMA) [10*n+2*(-1)^n-5: n in [1..70]];

(Python) [10*n+2*(-1)**n-5 for n in xrange(1, 70)]

(Julia) [10*n+2*(-1)^n-5 for n in 1:70] |> println

(PARI) apply(A322490(n)=10*n+2*(-1)^n-5, [1..70])

(PARI) Vec(x*(3 + 14*x + 3*x^2) / ((1 + x)*(1 - x)^2) + O(x^55)) \\ Colin Barker, Dec 13 2018

CROSSREFS

Cf. A004526, A056849.

Subsequence of A063226, A295009.

Similar sequences are listed in A322489.

Sequence in context: A082372 A273407 A267067 * A206626 A128107 A154620

Adjacent sequences:  A322487 A322488 A322489 * A322491 A322492 A322493

KEYWORD

nonn,base,easy

AUTHOR

Bruno Berselli, Dec 12 2018

STATUS

approved

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Last modified October 21 19:12 EDT 2019. Contains 328308 sequences. (Running on oeis4.)