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

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

Offset

1,2

Comments

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

For all i, j:

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

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

Links

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

Prog

(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);
A285732sq(n, k) = if(n==k, -n, if(n>k, A000027pairton(n-k, k), A000027pairton(n, k-n)));
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); };
v331306 = rgs_transform(A285732list(up_to));
A331306(n) = v331306[n];

Crossrefs

Cf. A003989, A072030, A285732.

Cf. also A331305, A331307.

Sequence in context: A093936 A329904 A331307 * A119353 A140859 A072586

Adjacent sequences: A331303 A331304 A331305 * A331307 A331308 A331309

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 19 2020

Status

approved