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 A098282 Iterate the map k -> A087712(k) starting at n; a(n) is the number of steps at which we see a repeated term for the first time; or -1 if the trajectory never repeats. 14
 1, 2, 3, 6, 4, 31, 7, 55, 4, 33, 5, 30, 32, 1, 4, 19, 8, 112, 56, 16, 27, 4, 4, 26, 2, 20, 223, 102, 34, 14, 6, 162, 2, 9, 10, 75, 31, 113, 21, 100, 33, 20, 2, 23, 30, 57, 5, 28, 24, 30, 224, 269, 20, 295, 11, 85, 103, 140, 9, 71, 113, 55, 34, 110, 76, 49, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The old entry with this A-number was a duplicate of A030298. a(52) is currently unknown. - Donovan Johnson a(52)-a(10000) were found using a conjunction of Mathematica and Kim Walisch's primecount program. The additional values of the prime-counting function can be found in the second a-file. - Matthew House, Dec 23 2016 LINKS Matthew House, Table of n, a(n) for n = 1..10000 Farideh Firoozbakht, Notes on the missing terms in this sequence Matthew House, Values found using primecount EXAMPLE 1 -> 1; 1 step to see a repeat, so a(1) = 1. 2 -> 1 -> 1; 2 steps to see a repeat. 3 -> 2 -> 1 -> 1; 3 steps to see a repeat. 4 -> 11 -> 5 -> 3 -> 2 -> 1 -> 1; 6 steps to see a repeat. 6 -> 12 -> 112 -> 11114 -> 1733 -> 270 -> 12223 -> 7128 -> 11122225 -> 33991010 -> 13913661 -> 2107998 -> 12222775 -> 33910130 -> 131212367 -> 56113213 -> 6837229 -> 4201627 -> 266366 -> 112430 -> 131359 -> 7981 -> 969 -> 278 -> 134 -> 119 -> 47 -> 15 -> 23 -> 9 -> 22 -> 15; 31 steps to see a repeat. 9 -> 22 -> 15 -> 23 -> 9; 4 steps to see a repeat. From David Applegate and N. J. A. Sloane, Feb 09 2009: (Start) The trajectories of the numbers 1 through 17, up to and including the first repeat, are as follows. Note that a(n) is one less than the number of terms shown. [1, 1] [2, 1, 1] [3, 2, 1, 1] [4, 11, 5, 3, 2, 1, 1] [5, 3, 2, 1, 1] [6, 12, 112, 11114, 1733, 270, 12223, 7128, 11122225, 33991010, 13913661, 2107998, 12222775, 33910130, 131212367, 56113213, 6837229, 4201627, 266366, 112430, 131359, 7981, 969, 278, 134, 119, 47, 15, 23, 9, 22, 15] [7, 4, 11, 5, 3, 2, 1, 1] [8, 111, 212, 1116, 112211, 52626, 124441, 28192, 11111152, 111165448, 1117261018, 1910112963, 252163429, 42205629, 2914219, 454002, 127605, 231542, 110938, 15631, 44510, 13605, 23155, 3582, 12246, 12637, 1509, 296, 11112, 111290, 131172, 1127117, 76613, 9470, 13161, 21328, 11111114, 14142115, 3625334, 1125035, 348169, 78151, 11369, 1373, 220, 1135, 349, 70, 134, 119, 47, 15, 23, 9, 22, 15] [9, 22, 15, 23, 9] [10, 13, 6, 12, 112, 11114, 1733, 270, 12223, 7128, 11122225, 33991010, 13913661, 2107998, 12222775, 33910130, 131212367, 56113213, 6837229, 4201627, 266366, 112430, 131359, 7981, 969, 278, 134, 119, 47, 15, 23, 9, 22, 15] [11, 5, 3, 2, 1, 1] [12, 112, 11114, 1733, 270, 12223, 7128, 11122225, 33991010, 13913661, 2107998, 12222775, 33910130, 131212367, 56113213, 6837229, 4201627, 266366, 112430, 131359, 7981, 969, 278, 134, 119, 47, 15, 23, 9, 22, 15] [13, 6, 12, 112, 11114, 1733, 270, 12223, 7128, 11122225, 33991010, 13913661, 2107998, 12222775, 33910130, 131212367, 56113213, 6837229, 4201627, 266366, 112430, 131359, 7981, 969, 278, 134, 119, 47, 15, 23, 9, 22, 15] [14, 14] [15, 23, 9, 22, 15] [16, 1111, 526, 156, 1126, 1103, 185, 312, 11126, 1734, 1277, 206, 127, 31, 11, 5, 3, 2, 1, 1] [17, 7, 4, 11, 5, 3, 2, 1, 1] For n = 18 see A077960. (End) MAPLE with(numtheory): f := proc(n) local t1, v, r, x, j; if (n = 1) then return 1; end if; t1 := ifactors(n): v := 0; for x in op(2, t1) do r := pi(x[1]): for j from 1 to x[2] do v := v * 10^length(r) + r; end do; end do; v; end proc; t := proc(n) local v, l, s; v := n; s := {v}; l := [v]; v := f(v); while not v in s do s := s union {v}; l := [op(l), v]; v := f(v); end do; [op(l), v]; end proc; [seq(nops(t(n))-1, n=1..17)]; # David Applegate and N. J. A. Sloane, Feb 09 2009 MATHEMATICA f[n_] := If[n==1, 1, FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n])]]; g[n_] := Length@ NestWhileList[f, n, UnsameQ, All] - 1; Array[g, 39] (* Robert G. Wilson v, Feb 02 2009; modified slightly by Farideh Firoozbakht, Feb 10 2009 *) PROG (GBnums) void ea (n) { mpz u[] ; // factors mpz tr[]; // sequence print(n); while(n > 1) { lfactors(u, n); // factorize into u vmap(u, pi); // replace factors by rank n = catv(u); // concatenate print(n); if(vsearch(tr, n) > 0) break; // loop found vpush(tr, n); // remember n } println(''); } // Jacques Tramu (Haskell) import Data.List (genericIndex) a098282 n = f [n] where f xs = if y `elem` xs then length xs else f (y:xs) where y = genericIndex (map a087712 [1..]) (head xs - 1) -- Reinhard Zumkeller, Jul 14 2013 CROSSREFS Cf. A087712, A007097, A077960. See also A145077, A145078, A145079, A144760, A144813, A144814, A144915, A144914. See A156055 for another version. Sequence in context: A156055 A096357 A091507 * A034855 A105214 A358940 Adjacent sequences: A098279 A098280 A098281 * A098283 A098284 A098285 KEYWORD nonn,base,nice AUTHOR Eric Angelini, Feb 02 2009 EXTENSIONS a(8) and a(10) found by Jacques Tramu Extended through a(39) by Robert G. Wilson v, Feb 02 2009 Terms through a(39) corrected by Farideh Firoozbakht, Feb 10 2009 a(40)-a(51) from Donovan Johnson, Jan 08 2011 More terms from and a(40) corrected by Matthew House, Dec 23 2016 STATUS approved

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Last modified March 5 05:10 EST 2024. Contains 370537 sequences. (Running on oeis4.)