A389897 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A007949(i) = A007949(j), A343029(i) = A343029(j) and A343030(i) = A343030(j) for all i, j >= 1.

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

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A322026(n), A361020(n)], or equally, of the quadruple [A007814(n), A007949(n), A343029(n), A343030(n)].

For all i, j >= 1:

a(i) = a(j) => A322026(i) = A322026(j),

a(i) = a(j) => A361020(i) = A361020(j),

a(i) = a(j) => A389896(i) = A389896(j).

Links

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

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);
A343029(n) = { my(t=1, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; };
A343030(n) = { my(t=0, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; };
Aux389897(n) = [A007814(n), A007949(n), A343029(n), A343030(n)];
v389897 = rgs_transform(vector(up_to, n, Aux389897(n)));
A389897(n) = v389897[n];

Crossrefs

Cf. A007814, A007949, A322026, A361020, A389897.

Cf. also A389898, A389899.

Sequence in context: A375245 A106618 A320113 * A387050 A080684 A159062

Adjacent sequences: A389894 A389895 A389896 * A389898 A389899 A389900

Keyword

nonn

Author

Antti Karttunen, Oct 19 2025

Status

approved