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A379004 Lexicographically earliest infinite sequence such that a(i) = a(j) => v_2(i) = v_2(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814) and v_5 (A112765) give the 2- and 5-adic valuations of n respectively.

%I A379004 #13 Dec 15 2024 12:58:14
%S A379004 1,2,1,3,4,2,1,5,1,6,1,3,1,2,4,7,1,2,1,8,1,2,1,5,9,2,1,3,1,6,1,10,1,2,
%T A379004 4,3,1,2,1,11,1,2,1,3,4,2,1,7,1,12,1,3,1,2,4,5,1,2,1,8,1,2,1,13,4,2,1,
%U A379004 3,1,6,1,5,1,2,9,3,1,2,1,14,1,2,1,3,4,2,1,5,1,6,1,3,1,2,4,10,1,2,1,15,1,2,1,5,4
%N A379004 Lexicographically earliest infinite sequence such that a(i) = a(j) => v_2(i) = v_2(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814) and v_5 (A112765) give the 2- and 5-adic valuations of n respectively.
%C A379004 Restricted growth sequence transform of A132741, or equally, of the ordered pair [A007814(n), A112765(n)].
%C A379004 For all i, j:
%C A379004   A379005(i) = A379005(j) => a(i) = a(j).
%C A379004 A379003 (after its initial 0) and this sequence are ordinal transforms of each other.
%H A379004 Antti Karttunen, <a href="/A379004/b379004.txt">Table of n, a(n) for n = 1..100000</a>
%o A379004 (PARI)
%o A379004 up_to = 100000;
%o A379004 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 A379004 v379004 = rgs_transform(vector(up_to, n, [valuation(n,2), valuation(n,5)]));
%o A379004 A379004(n) = v379004[n];
%Y A379004 Cf. A007814, A112765, A132741, A379003 (ordinal transform), A379005.
%K A379004 nonn,look
%O A379004 1,2
%A A379004 _Antti Karttunen_, Dec 15 2024