A340382 - OEIS

%I #6 Jan 16 2021 06:39:36

%S 1,2,1,2,1,3,2,2,1,2,2,4,1,3,2,2,1,2,1,2,1,4,2,4,3,5,2,4,2,5,2,2,2,2,

%T 1,2,2,3,2,2,2,2,3,4,2,3,1,4,4,6,2,6,1,7,2,4,2,4,1,6,2,4,2,2,4,3,1,2,

%U 3,3,1,2,1,6,2,4,3,4,2,2,4,4,2,2,2,6,5,4,2,4,1,4,1,8,1,4,3,9,2,6,3,6,2,6,2

%N Lexicographically earliest  infinite sequence such that a(i) = a(j) => A278222(A291759(i)) = A278222(A291759(j)), for all i, j >= 1.

%H Antti Karttunen, <a href="/A340382/b340382.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

%o A048673(n) = (A003961(n)+1)/2;

%o A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814

%o A291759(n) = A289814(A048673(n));

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

%o A278222(n) = A046523(A005940(1+n));

%o 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; };

%o v340382 = rgs_transform(vector(up_to,n,A278222(A291759(n))));

%o A340382(n) = v340382[n];

%Y Cf. A278222, A291759, A304748, A340381,

%Y Cf. A340377 (positions of ones).

%Y Cf. also A305302.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 16 2021