A098282 - OEIS

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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.

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, 80, 33, 20, 2, 23, 30, 57, 5, 28, 24, 30, 224 (list; graph; refs; listen; history; 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`
	LINKS	`Farideh Firoozbakht, Notes on the missing terms in this sequence`
	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.` `Comment from David Applegate and N. J. A. Sloane (njas(AT)research.att.com), 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	`(Maple program from David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Feb 09 2009) (Start) 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)]; (End)`
	MATHEMATICA	`(Mma program from Robert G. Wilson, v (rgwv(AT)rgwv.com), Feb 02 2009; modified slightly by Farideh Firoozbakht (mymontain(AT)yahoo.com), Feb 10 2009)` `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]`
	PROG	`(GBnums code from Jacques Tramu (jacques.tramu(AT)echolalie.com)):` `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('');` `}`
	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 A136315` `Adjacent sequences: A098279 A098280 A098281 * A098283 A098284 A098285`
	KEYWORD	`nonn,base,more,nice`
	AUTHOR	`Eric Angelini (Eric.Angelini(AT)kntv.be), Feb 02 2009`
	EXTENSIONS	`Jacques Tramu found a(8) and a(10).` `Extended through a(39) by Robert G. Wilson, v (rgwv(AT)rgwv.com), Feb 02 2009.` `Terms through a(39) corrected by Farideh Firoozbakht (mymontain(AT)yahoo.com), Feb 10 2009` `a(40)-a(51) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 08 2011`

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Last modified February 13 03:07 EST 2012. Contains 205435 sequences.