A322026 Lexicographically earliest such sequence a that a(i) = a(j) => A007814(i) = A007814(j) and A007949(i) = A007949(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation of n.

1, 2, 3, 4, 1, 5, 1, 6, 7, 2, 1, 8, 1, 2, 3, 9, 1, 10, 1, 4, 3, 2, 1, 11, 1, 2, 12, 4, 1, 5, 1, 13, 3, 2, 1, 14, 1, 2, 3, 6, 1, 5, 1, 4, 7, 2, 1, 15, 1, 2, 3, 4, 1, 16, 1, 6, 3, 2, 1, 8, 1, 2, 7, 17, 1, 5, 1, 4, 3, 2, 1, 18, 1, 2, 3, 4, 1, 5, 1, 9, 19, 2, 1, 8, 1, 2, 3, 6, 1, 10, 1, 4, 3, 2, 1, 20, 1, 2, 7, 4, 1, 5, 1, 6, 3

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A007814(n), A007949(n)].

For all i, j:

A305900(i) = A305900(j) => a(i) = a(j),

a(i) = a(j) => A122841(i) = A122841(j),

a(i) = a(j) => A244417(i) = A244417(j),

a(i) = a(j) => A322316(i) = A322316(j) => A072078(i) = A072078(j).

If and only if a(k) > a(i) for all k > i then k is in A003586, - David A. Corneth, Dec 03 2018

That is, A003586 gives the positions of records (1, 2, 3, 4, 5, ...) in this sequence.

Sequence A126760 (without its initial zero) and this sequence are ordinal transforms of each other.

Links

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

Formula

For s = A003586(n), a(s) = n = a((6k+1)*s) = a((6k-1)*s), where s is the n-th 3-smooth number and k > 0. - David A. Corneth, Dec 03 2018

A065331(n) = A003586(a(n)). - David A. Corneth, Dec 04 2018

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);
v322026 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n)]));
A322026(n) = v322026[n];

Crossrefs

Cf. A003586 (positions of records, the first occurrence of n), A007814, A007949, A065331, A072078, A087465, A122841, A126760 (ordinal transform), A322316.

Cf. also A247714 and A255975.

Sequence in context: A319826 A278108 A302786 * A363247 A087165 A238326

Adjacent sequences: A322023 A322024 A322025 * A322027 A322028 A322029

Keyword

nonn

Author

Antti Karttunen, Dec 03 2018

Status

approved