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 A003598 Numbers of the form 5^i * 11^j. 22
 1, 5, 11, 25, 55, 121, 125, 275, 605, 625, 1331, 1375, 3025, 3125, 6655, 6875, 14641, 15125, 15625, 33275, 34375, 73205, 75625, 78125, 161051, 166375, 171875, 366025, 378125, 390625, 805255, 831875, 859375, 1771561, 1830125, 1890625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA An asymptotic formula for a(n) is roughly 1/sqrt(55)*exp(sqrt(2*log(5)*log(11)*n)). - Benoit Cloitre, Mar 08 2002 The characteristic function of this sequence is given by Sum_{n >= 1} x^a(n) = Sum_{n >= 1} mu(55*n)*x^n/(1 - x^n), where mu(n) is the Möbius function A008683. Cf. with the formula of Hanna in A051037. - Peter Bala, Mar 18 2019 MATHEMATICA Take[Union[(5^#[[1]] 11^#[[2]])&/@Tuples[Range[0, 20], {2}]], 50]  (* Harvey P. Dale, Dec 26 2010 *) fQ[n_]:=PowerMod[55, n, n] == 0; Select[Range[2*10^6], fQ] (* Vincenzo Librandi, Jun 27 2016 *) PROG (PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(11), N=11^n; while(N<=lim, listput(v, N); N*=5)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011 (Haskell) import Data.Set (singleton, deleteFindMin, insert) a003598 n = a003598_list !! (n-1) a003598_list = f \$ singleton (1, 0, 0) where    f s = y : f (insert (5 * y, i + 1, j) \$ insert (11 * y, i, j + 1) s')          where ((y, i, j), s') = deleteFindMin s -- Reinhard Zumkeller, May 15 2015 (MAGMA) [n: n in [1..2*10^6] | PrimeDivisors(n) subset [5, 11]]; // Vincenzo Librandi, Jun 27 2016 (GAP) Filtered([1..2*10^6], n->PowerMod(55, n, n)=0); # Muniru A Asiru, Mar 19 2019 (Sage) [n for n in (1..2*10^6) if power_mod(55, n, n)==0] # G. C. Greubel, Mar 19 2019 CROSSREFS Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003596, A003597, A107988, A108698, A003599, A107788, A108687, A108779, A108090. Sequence in context: A167238 A084640 A056739 * A014858 A018368 A050344 Adjacent sequences:  A003595 A003596 A003597 * A003599 A003600 A003601 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 21 01:26 EDT 2019. Contains 323429 sequences. (Running on oeis4.)