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A286626
Restricted growth sequence computed for primorial base related filter-sequence A278226.
20
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
0,2
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).
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 *)
PROG
(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; };
write_to_bfile(0, rgs_transform(vector(30031, n, A278226(n-1))), "b286626.txt");
CROSSREFS
Cf. also A101296, A286603, A286605, A286610, A286619, A286621, A286622, A286378 for similarly constructed sequences.
Sequence in context: A111263 A357378 A351257 * A328628 A328629 A342022
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, May 11 2017
STATUS
approved