A331306 -id:A331306 - cp's OEIS frontend

A331305 Lexicographically earliest infinite sequence such that a(i) = a(j) => A286153(i) = A286153(j) for all i, j.

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

Offset: 1

Antti Karttunen, Jan 19 2020

Restricted growth sequence transform of A286153 (when considered as an one-dimensional sequence), or equally, of A286155.
For all i, j:
  a(i) = a(j) => A091255(i) = A091255(j).

Antti Karttunen, Table of n, a(n) for n = 1..25425
Index entries for sequences related to polynomials in ring GF(2)[X]

Cf. A091255, A286153, A286155.

Cf. also A331306, A331307.

up_to = 25425; \\ = binomial(225+1,2)
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; };
A001477pairton(a,b) = (((a+b)^2 + 3*a + b)/2);
A286153sq(n, k) = if(n>k,A001477pairton(bitxor(n,k),k),A001477pairton(n,bitxor(n,k)));
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); };
v331305 = rgs_transform(A286153list(up_to));
A331305(n) = v331305[n]; \\ Antti Karttunen, Jan 19 2020

A331307 Lexicographically earliest infinite sequence such that for all i, j: a(i) = a(j) => f(i) = f(j), where f(n) = A285722(n), except f(1) = -1.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 6, 5, 3, 7, 8, 9, 4, 9, 10, 11, 12, 7, 6, 13, 14, 15, 16, 13, 4, 12, 17, 18, 19, 20, 21, 10, 8, 21, 22, 23, 24, 25, 26, 17, 4, 16, 27, 28, 29, 30, 31, 32, 27, 14, 11, 26, 33, 34, 35, 36, 37, 38, 39, 22, 4, 20, 39, 40, 41, 42, 43, 44, 45, 46, 33, 18, 15, 32, 47, 48, 49, 50, 51, 52, 53, 54, 47, 28, 4, 25, 46, 55, 56, 57, 58, 59, 60, 61, 62, 63, 40, 23, 19, 38

Offset: 1

Antti Karttunen, Jan 19 2020

Restricted growth sequence transform of function: f(1) = -1, and for n>1, f(n) = A285722(n), when the latter is considered as an one-dimensional sequence.
For all i, j:
  A331306(i) = A331306(j) => a(i) = a(j) => A072030(i) = A072030(j).

Antti Karttunen, Table of n, a(n) for n = 1..25425

Cf. A072030, A285722.

Cf. also A331305, A331306.

up_to = 25425; \\ = binomial(225+1,2)
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; };
A000027pairton(a,b) = ((2+((a+b)^2 - a) - (3*b))/2);
A285722sq(n, k) = if(n==k,0,if(n>k,A000027pairton(n-k,k),A000027pairton(n,k-n)));
A285722list(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] = A285722sq(col,(a-(col-1))))); (v); };
v285722 = A285722list(up_to);
A285722(n) = v285722[n];
A331307aux(n) = if(1==n,-n,A285722(n));
v331307 = rgs_transform(vector(up_to, n, A331307aux(n)));
A331307(n) = v331307[n];

cp's OEIS Frontend

A331305 Lexicographically earliest infinite sequence such that a(i) = a(j) => A286153(i) = A286153(j) for all i, j.

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