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 A304101 Restricted growth sequence transform of A278222(A048679(n)). 12
 1, 2, 2, 2, 3, 2, 4, 3, 2, 4, 4, 3, 5, 2, 4, 4, 4, 6, 3, 6, 5, 2, 4, 4, 4, 6, 4, 7, 6, 3, 6, 6, 5, 8, 2, 4, 4, 4, 6, 4, 7, 6, 4, 7, 7, 6, 9, 3, 6, 6, 6, 10, 5, 9, 8, 2, 4, 4, 4, 6, 4, 7, 6, 4, 7, 7, 6, 9, 4, 7, 7, 7, 11, 6, 11, 9, 3, 6, 6, 6, 10, 6, 11, 10, 5, 9, 9, 8, 12, 2, 4, 4, 4, 6, 4, 7, 6, 4, 7, 7, 6, 9, 4, 7, 7, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Positions of 2's is given by the positive Fibonacci numbers: 1, 2, 3, 5, 8, 13, 21, ..., that is, A000045(n) from n >= 2 onward. Positions of 3's is given by Lucas numbers larger than 3: 4, 7, 11, 18, ..., that is, A000032(n) from n >= 3 onward. Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A048679(n). Compare to the scatter plot of A286622. LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 PROG (PARI) rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; }; A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649 A003714(n) = { my(s=0, w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); } A106151(n) = if(n<=1, n, if(n%2, 1+(2*A106151((n-1)/2)), A106151(n>>valuation(n, 2))<<(valuation(n, 2)-1))); A048679(n) = if(!n, n, A106151(2*A003714(n))); A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523 A278222(n) = A046523(A005940(1+n)); v304101 = rgs_transform(vector(1+up_to, n, A278222(A048679(n-1)))); A304101(n) = v304101[1+n]; CROSSREFS Cf. A000032, A000045, A003603, A007895, A035513, A048679, A278222, A304100, A304102, A304103, A304104, A304105. Cf. also A286622 (compare the scatter-plots). Sequence in context: A233539 A317223 A321576 * A278636 A126336 A134446 Adjacent sequences:  A304098 A304099 A304100 * A304102 A304103 A304104 KEYWORD nonn,look AUTHOR Antti Karttunen, May 13 2018 STATUS approved

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Last modified July 21 22:02 EDT 2019. Contains 325210 sequences. (Running on oeis4.)