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.

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

Author

Antti Karttunen, Jan 19 2020

Keywords

• nonn
• tabl

Comments

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).

Links

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

Crossrefs

Cf. A072030, A285722.

Cf. also A331305, A331306.

Programs

PARI

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];