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 A064385 a(n) = 2*5^n - 3. 1
 7, 47, 247, 1247, 6247, 31247, 156247, 781247, 3906247, 19531247, 97656247, 488281247, 2441406247, 12207031247, 61035156247, 305175781247, 1525878906247, 7629394531247, 38146972656247 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). 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. LINKS Harry J. Smith, Table of n, a(n) for n=1,...,100 Index entries for linear recurrences with constant coefficients, signature (6,-5). FORMULA From Vincenzo Librandi, Nov 12 2011: (Start) a(n) = 5*a(n-1) + 12. a(n) = 6*a(n-1) - 5*a(n-2). G.f.: (2 - 5*x + 15*x^2)/((1-x)*(1-5*x)). (End) MAPLE 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; PROG (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))) (PARI) { for (n=1, 100, write("b064385.txt", n, " ", 2*5^n - 3) ) } \\ Harry J. Smith, Sep 13 2009 (Magma) [2*5^n-3: n in [1..30]]; // Vincenzo Librandi, Nov 12 2011 CROSSREFS Sequence in context: A009202 A093112 A091516 * A269520 A009260 A201871 Adjacent sequences: A064382 A064383 A064384 * A064386 A064387 A064388 KEYWORD nonn,easy AUTHOR Daniel Dockery (drd(AT)peritus.virtualave.net), Sep 16 2001 STATUS approved

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Last modified May 30 14:11 EDT 2023. Contains 363055 sequences. (Running on oeis4.)