A286626 Restricted growth sequence computed for primorial base related filter-sequence A278226.

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, 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, 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

Offset: 0

Author

Antti Karttunen, May 11 2017

Keywords

• nonn
• look

Comments

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).

For example, for all i, j: a(i) = a(j) => A276150(i) = A276150(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial base

Crossrefs

Cf. A278226, A276150.

Cf. also A101296, A286603, A286605, A286610, A286619, A286621, A286622, A286378 for similarly constructed sequences.

Programs

Mathematica

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 *)

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])); }
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
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; };
A278226(n) = A046523(A276086(n));
write_to_bfile(0,rgs_transform(vector(30031,n,A278226(n-1))),"b286626.txt");