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%I #17 May 14 2017 15:56:00
%S 1,2,2,3,4,5,2,3,3,6,5,7,4,5,5,7,8,9,10,11,11,12,13,14,15,16,16,17,18,
%T 19,2,3,3,6,5,7,3,6,6,20,7,21,5,7,7,21,9,22,11,12,12,23,14,24,16,17,
%U 17,25,19,26,4,5,5,7,8,9,5,7,7,21,9,22,8,9,9,22,27,28,13,14,14,24,29,30,18,19,19,26,31,32,10,11,11,12,13,14,11,12,12,23,14,24
%N Restricted growth sequence computed for primorial base related filter-sequence A278226.
%C When filtering sequences (by equivalence class partitioning), this sequence (with its modestly sized terms) can be used instead of A278226, because for all i, j it holds that: a(i) = a(j) <=> A278226(i) = A278226(j).
%C For example, for all i, j: a(i) = a(j) => A276150(i) = A276150(j).
%H Antti Karttunen, <a href="/A286626/b286626.txt">Table of n, a(n) for n = 0..30030</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%t b = MixedRadix[Reverse@ Prime@ Range@ 12]; f[n_] := Times @@ MapIndexed[Prime[#2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]] - Boole[n == 1]; With[{nn = 102}, Function[s, Table[Position[Keys@ s, k_ /; MemberQ[k, n]][[1, 1]], {n, nn}]]@ Map[#1 -> #2 & @@ # &, Transpose@ {Values@ #, Keys@ #}] &@ PositionIndex@ Table[Function[k, f[Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ k, Reverse@ k}]]@ IntegerDigits[n, b], {n, 0, nn}]] (* _Michael De Vlieger_, May 12 2017, Version 10.2 *)
%o (PARI)
%o 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; };
%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A278226(n) = A046523(A276086(n));
%o write_to_bfile(0,rgs_transform(vector(30031,n,A278226(n-1))),"b286626.txt");
%Y Cf. A278226, A276150.
%Y Cf. also A101296, A286603, A286605, A286610, A286619, A286621, A286622, A286378 for similarly constructed sequences.
%K nonn,look
%O 0,2
%A _Antti Karttunen_, May 11 2017
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