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 A336312 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336120(i)) = A278222(A336120(j)) for all i, j >= 1. 5
 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 4, 1, 2, 2, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 2, 3, 1, 2, 1, 2, 1, 2, 1, 4, 2, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 4, 1, 2, 1, 2, 2, 2, 1, 3, 1, 4, 1, 2, 1, 2, 2, 4, 1, 3, 1, 3, 1, 3, 1, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Restricted growth sequence transform of A278222(A336120(n)). For all i, j:   a(i) = a(j) => A336121(i) = A336121(j) => A335909(i) = A335909(j). LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 PROG (PARI) up_to = 1024; \\ 65537; 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; }; \\ Needs also code from A336124: A253553(n) = if(n<=2, 1, my(f=factor(n), k=#f~); if(f[k, 2]>1, f[k, 2]--, f[k, 1] = precprime(f[k, 1]-1)); factorback(f)); A336120(n) = if(1==n, 0, (3==A336124(n))+(2*A336120(A253553(n)))); A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940 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)); v336312 = rgs_transform(vector(up_to, n, A278222(A336120(n)))); A336312(n) = v336312[n]; CROSSREFS Cf. A336311, A336313. Cf. A336119 (positions of ones). Cf. also A292583, A332901, A335909, A336121. Sequence in context: A161279 A160983 A322354 * A161237 A161061 A161265 Adjacent sequences:  A336309 A336310 A336311 * A336313 A336314 A336315 KEYWORD nonn AUTHOR Antti Karttunen, Jul 17 2020 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)