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A331306 Lexicographically earliest infinite sequence such that a(i) = a(j) => A285732(i) = A285732(j) for all i, j. 3

%I #7 Jan 19 2020 20:38:15

%S 1,2,2,3,4,5,6,5,3,7,8,9,10,9,11,12,13,7,6,14,15,16,17,14,18,13,19,20,

%T 21,22,23,11,8,23,24,25,26,27,28,19,29,17,30,31,32,33,34,35,30,15,12,

%U 28,36,37,38,39,40,41,42,24,43,22,42,44,45,46,47,48,49,50,36,20,16,35,51,52,53,54,55,56,57,58,51,31,59,27,50,60,61,62,63,64,65,66,67,68,44,25,21,41

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A285732(i) = A285732(j) for all i, j.

%C Restricted growth sequence transform of A285732 (when considered as an one-dimensional sequence).

%C For all i, j:

%C a(i) = a(j) => A003989(i) = A003989(j),

%C a(i) = a(j) => A331307(i) = A331307(j) => A072030(i) = A072030(j).

%H Antti Karttunen, <a href="/A331306/b331306.txt">Table of n, a(n) for n = 1..25425</a>

%o (PARI)

%o up_to = 25425; \\ = binomial(225+1,2)

%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 A000027pairton(a,b) = ((2+((a+b)^2 - a) - (3*b))/2);

%o A285732sq(n, k) = if(n==k,-n,if(n>k,A000027pairton(n-k,k),A000027pairton(n,k-n)));

%o A285732list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A285732sq(col,(a-(col-1))))); (v); };

%o v331306 = rgs_transform(A285732list(up_to));

%o A331306(n) = v331306[n];

%Y Cf. A003989, A072030, A285732.

%Y Cf. also A331305, A331307.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Jan 19 2020

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