A340381 - OEIS

%I #6 Jan 16 2021 06:39:28

%S 1,2,1,1,3,2,2,3,4,1,1,1,1,1,2,4,5,3,3,5,5,2,1,3,1,2,1,5,5,1,1,6,1,1,

%T 4,7,1,1,7,7,3,1,2,1,5,3,1,4,1,2,5,1,5,2,5,7,3,1,7,5,5,2,5,8,2,5,3,5,

%U 1,3,7,9,6,2,4,5,2,3,3,10,11,1,1,5,4,1,2,3,7,1,10,7,7,2,1,6,1,2,1,1,5,1,2,3,7

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A304759(i)) = A278222(A304759(j)), for all i, j >= 1.

%C For all i, j: A304758(i) = A304758(j) => a(i) = a(j) => A340378(i) = A340378(j).

%H Antti Karttunen, <a href="/A340381/b340381.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 A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813

%o A304759(n) = A289813(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 v340381 = rgs_transform(vector(up_to,n,A278222(A304759(n))));

%o A340381(n) = v340381[n];

%Y Cf. A278222, A304758, A304759, A340378, A340382, A340383.

%Y Cf. A340376 (positions of 2's).

%Y Cf. also A305301.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 16 2021