A379005 - OEIS

%I #13 Dec 15 2024 12:11:48

%S 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,

%T 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,

%U 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

%N 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.

%C Restricted growth sequence transform of A355582.

%C For all i, j:

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

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

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

%H Antti Karttunen, <a href="/A379005/b379005.txt">Table of n, a(n) for n = 1..100000</a>

%o (PARI)

%o up_to = 100000;

%o 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; };

%o v379005 = rgs_transform(vector(up_to, n, [valuation(n,2), valuation(n,3), valuation(n,5)]));

%o A379005(n) = v379005[n];

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

%Y Cf. A322026, A379001, A379004.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 15 2024