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 A064385 a(n) = 2*5^n - 3. 1

%I #14 Sep 08 2022 08:45:04

%S 7,47,247,1247,6247,31247,156247,781247,3906247,19531247,97656247,

%T 488281247,2441406247,12207031247,61035156247,305175781247,

%U 1525878906247,7629394531247,38146972656247

%N a(n) = 2*5^n - 3.

%C 5th polygonal numbers for polygons of 5^n sides divided by 5: p(5,5^x)/5, where p(n,k) = (n/2)*(n*k - k + 4 - 2*n).

%C This sequence exhibits periodic digit repetition; e.g. the last digit repeats as 7, the penultimate as 4 and the antepenultimate as 2, all with a period of 1; the fourth-to-last digit repeats the sequence 1, 6 with a period of 2; the fifth-to-last repeats the sequence 3, 5, 8, 0; the sixth-to-last repeats 1, 7, 9, 5, 6, 2, 4, 0. And so on, it seems, for the other digits as the numbers grow.

%H Harry J. Smith, <a href="/A064385/b064385.txt">Table of n, a(n) for n=1,...,100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).

%F From _Vincenzo Librandi_, Nov 12 2011: (Start)

%F a(n) = 5*a(n-1) + 12.

%F a(n) = 6*a(n-1) - 5*a(n-2).

%F G.f.: (2 - 5*x + 15*x^2)/((1-x)*(1-5*x)).

%F (End)

%p p := proc(n,k) (n/2)*(n*k-k+4-2*n) end: for x from 1 to 19 do p(5,5^x)/5 od; q := proc(x) 2*5^x-3 end: for x from 1 to 19 do q(x) od;

%o (PARI) p(n,k) = (n/2)*(n*k-k+4-2*n) for(x=1,19,print(p(5,5^x)/5)) q(x) = 2*5^x-3 for(x=1,19,print(q(x)))

%o (PARI) { for (n=1, 100, write("b064385.txt", n, " ", 2*5^n - 3) ) } \\ _Harry J. Smith_, Sep 13 2009

%o (Magma) [2*5^n-3: n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2011

%K nonn,easy

%O 1,1

%A Daniel Dockery (drd(AT)peritus.virtualave.net), Sep 16 2001

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Last modified September 23 17:20 EDT 2023. Contains 365554 sequences. (Running on oeis4.)