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A286610
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Restricted growth sequence computed for Euler totient function phi, A000010.
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10
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1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 5, 3, 6, 4, 7, 7, 8, 4, 9, 7, 6, 5, 10, 7, 11, 6, 9, 6, 12, 7, 13, 8, 11, 8, 14, 6, 15, 9, 14, 8, 16, 6, 17, 11, 14, 10, 18, 8, 17, 11, 19, 14, 20, 9, 16, 14, 15, 12, 21, 8, 22, 13, 15, 19, 23, 11, 24, 19, 25, 14, 26, 14, 27, 15, 16, 15, 22, 14, 28, 19, 29, 16, 30, 14, 31, 17, 32, 16, 33, 14, 27, 25, 22, 18, 27, 19, 34, 17, 22
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Construction: we start with a(1)=1 for phi(1)=1 (where phi = A000010), and then after, for all n > 1, whenever the value of phi(n) has not been encountered before, we set a(n) to the least natural number k not already in sequence among a(1) .. a(n-1), otherwise [whenever phi(n) = phi(m), for some m < n], we set a(n) = a(m), i.e., to the same value that was assigned to a(m).
For n=2, phi(2) = 1, which value was already encountered as phi(1), thus we set also a(2) = 1.
For n=3, phi(3) = 2, which has not been encountered before, thus we allot for a(3) the least so far unused number, which is 2, thus a(3) = 2.
For n=4, phi(4) = 2, which was already encountered as at n=3 for the first time, thus we set a(4) = a(3) = 2.
For n=5, phi(5) = 4, which has not been encountered before, thus we allot for a(5) the least so far unused number, which is now 3, thus a(5) = 3.
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MATHEMATICA
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With[{nn = 99}, Function[s, Table[Position[Keys@ s, k_ /; MemberQ[k, n]][[1, 1]], {n, nn}]]@ Map[#1 -> #2 & @@ # &, Transpose@ {Values@ #, Keys@ #}] &@ PositionIndex@ Array[EulerPhi, nn]] (* Michael De Vlieger, May 12 2017, Version 10 *)
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PROG
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(PARI)
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences, invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences, invec[i], i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
write_to_bfile(1, rgs_transform(vector(10000, n, A000010(n))), "b286610.txt");
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CROSSREFS
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Cf. A000010, A210719 (positions of records, and also the first occurrence of each n).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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