A331305 - OEIS

%I #13 Dec 10 2020 01:33:19

%S 1,2,3,4,5,6,7,6,4,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,

%T 25,26,27,28,29,13,9,30,31,32,33,34,35,25,36,21,37,38,39,40,41,42,37,

%U 30,29,35,43,44,45,46,47,48,49,31,50,28,51,52,53,54,55,56,57,58,59,26,20,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79

%N Lexicographically  earliest infinite sequence such that a(i) = a(j) => A286153(i) = A286153(j) for all i, j.

%C Restricted growth sequence transform of A286153 (when considered as an one-dimensional sequence), or equally, of A286155.

%C For all i, j:

%C   a(i) = a(j) => A091255(i) = A091255(j).

%H Antti Karttunen, <a href="/A331305/b331305.txt">Table of n, a(n) for n = 1..25425</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</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 A001477pairton(a,b) = (((a+b)^2 + 3*a + b)/2);

%o A286153sq(n, k) = if(n>k,A001477pairton(bitxor(n,k),k),A001477pairton(n,bitxor(n,k)));

%o A286153list(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] = A286153sq(col,(a-(col-1))))); (v); };

%o v331305 = rgs_transform(A286153list(up_to));

%o A331305(n) = v331305[n]; \\ _Antti Karttunen_, Jan 19 2020

%Y Cf. A091255, A286153, A286155.

%Y Cf. also A331306, A331307.

%K nonn,tabl,look

%O 1,2

%A _Antti Karttunen_, Jan 19 2020