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A271390 a(n) = (2*n + 1)^(2*floor((n-1)/2) + 1). 1
1, 3, 5, 343, 729, 161051, 371293, 170859375, 410338673, 322687697779, 794280046581, 952809757913927, 2384185791015625, 4052555153018976267, 10260628712958602189, 23465261991844685929951, 59938945498865420543457, 177482997121587371826171875, 456487940826035155404146917 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

All members are odd, therefore:

........................

|   k   |  a(n) mod k  |

|.......|..............|

|  n+1  |  A001477(n)  |

| 2*n+2 |  A005408(n)  |

|   2   |  A000012(n)  |

|   3   |  A080425(n+2)|

|   4   |  A010684(n)  |

|   6   |  A130793(n)  |

........................

Final digit of (2*n + 1)^(2*floor((n-1)/2) + 1) gives periodic sequence -> period 20: repeat [1,3,5,3,9,1,3,5,3,9,1,7,5,7,9,1,7,5,7,9], defined by the recurrence relation b(n) = b(n-2) - b(n-4) + b(n+5) + b(n+6) - b(n-7) - b(n-8) + b(n-9) - b(n-11) + b(n-13).

LINKS

Ilya Gutkovskiy, Table of n, a(n) for n = 0..75

FORMULA

a(n) = (2*n + 1)^(n - 1 + (1 + (-1)^(n-1))/2).

a(n) = A005408(n)^A109613(n-1).

a(n) = (2*n + 1)^(n - 1/2 - (-1)^n/2). - Wesley Ivan Hurt, Apr 10 2016

EXAMPLE

a(0) =  1;

a(1) =  3^1 = 3;

a(2) =  5^1 = 5;

a(3) =  7^3 = 343;

a(4) =  9^3 = 729;

a(5) = 11^5 = 161051;

a(6) = 13^5 = 371293;

a(7) = 15^7 = 170859375;

a(8) = 17^7 = 410338673;

...

a(10000) = 1.644...*10^43006;

...

a(100000) = 8.235...*10^530097, etc.

This sequence can be represented as a binary tree:

                                    1

                 ................../ \..................

                3^1                                   5^1

     7^3......../ \......9^3                11^5....../ \.......13^5

     / \                 / \                 / \                 / \

    /   \               /   \               /   \               /   \

   /     \             /     \             /     \             /     \

15^7    17^7        19^9    21^9        23^11   25^11       27^13   29^13

MAPLE

A271390:=n->(2*n + 1)^(n - 1/2 - (-1)^n/2): seq(A271390(n), n=0..30); # Wesley Ivan Hurt, Apr 10 2016

MATHEMATICA

Table[(2 n + 1)^(2 Floor[(n - 1)/2] + 1), {n, 0, 18}]

Table[(2 n + 1)^(n - 1 + (1 + (-1)^(n - 1))/2), {n, 0, 18}]

PROG

(PARI) a(n) = (2*n + 1)^(2*((n-1)\2) + 1); \\ Altug Alkan, Apr 06 2016

(Python)

for n in range(0, 10**3):print((int)((2*n+1)**(2*floor((n-1)/2)+1)))

# Soumil Mandal, Apr 10 2016

CROSSREFS

Cf. A005408, A092503, A109613.

Sequence in context: A309740 A280035 A087670 * A138584 A277995 A247699

Adjacent sequences:  A271387 A271388 A271389 * A271391 A271392 A271393

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Apr 06 2016

STATUS

approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)