A379005 Lexicographically earliest infinite sequence such that a(i) = a(j) => v_2(i) = v_2(j), v_3(i) = v_3(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814), v_3 (A007949) and v_5 (A112765) give the 2-, 3- and 5-adic valuations of n respectively.

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

Offset

1,2

Comments

Restricted growth sequence transform of A355582.

For all i, j:

A379001(i) = A379001(j) => a(i) = a(j),

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

a(i) = a(j) => A379004(i) = A379004(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Prog

(PARI)
up_to = 100000;
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; };
v379005 = rgs_transform(vector(up_to, n, [valuation(n, 2), valuation(n, 3), valuation(n, 5)]));
A379005(n) = v379005[n];

Crossrefs

Cf. A007814, A007949, A112765, A355582, A379006 (ordinal transform).

Cf. A322026, A379001, A379004.

Sequence in context: A243733 A334618 A138776 * A339738 A364500 A280701

Adjacent sequences: A379002 A379003 A379004 * A379006 A379007 A379008

Keyword

nonn

Author

Antti Karttunen, Dec 15 2024

Status

approved