A353277 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A020639(n), A341353(n)], with f(1) = 1.

1, 2, 3, 4, 5, 2, 6, 2, 7, 8, 9, 2, 10, 2, 3, 4, 11, 2, 12, 2, 13, 4, 14, 2, 15, 2, 3, 2, 16, 4, 17, 2, 3, 4, 5, 18, 19, 2, 7, 4, 20, 2, 21, 2, 3, 18, 22, 2, 23, 2, 3, 2, 24, 2, 25, 2, 7, 2, 26, 2, 27, 4, 3, 8, 5, 4, 28, 2, 3, 2, 29, 2, 30, 2, 3, 2, 6, 2, 31, 2, 7, 4, 32, 4, 15, 2, 33, 18, 34, 8, 35, 2, 3, 8, 5, 2

Offset

1,2

Comments

Restricted growth sequence transform of function f(1) = 1, and for n > 1, f(n) = [A007814(u), A007949(u)], where u = A156552(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Prog

(PARI)
up_to = 65537;
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; };
A007814(n) = valuation(n, 2);
A007949(n) = valuation(n, 3);
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
Aux353277(n) = if(1==n, 1, my(u=A156552(n)); [A007814(u), A007949(u)]);
v353277 = rgs_transform(vector(up_to, n, Aux353277(n)));
A353277(n) = v353277[n];

Crossrefs

Cf. A007814, A007949, A020639, A156552, A341353, A353278 (ordinal transform).

Cf. also A322026, A340680, A341355.

Sequence in context: A043265 A194459 A143120 * A308201 A026362 A223490

Adjacent sequences: A353274 A353275 A353276 * A353278 A353279 A353280

Keyword

nonn

Author

Antti Karttunen, Apr 10 2022

Status

approved