cp's OEIS Frontend

A319689 Number of distinct values of A078898 that occur when map x -> A064989(x) is iterated, starting from x = n, until an even number is reached; a(1) = 0 by convention.

%I A319689 #13 Nov 21 2018 09:23:49
%S A319689 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,
%T A319689 1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,2,1,3,1,1,1,
%U A319689 2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,3,1,2,1,1,1,2,1,2,1,3,1,1,1,2,1,1,1,1,1,2
%N A319689 Number of distinct values of A078898 that occur when map x -> A064989(x) is iterated, starting from x = n, until an even number is reached; a(1) = 0 by convention.
%C A319689 Number of distinct values that A078898 obtains when applied to n and all the terms above it in that column where it is located in array A246278.
%H A319689 Antti Karttunen, <a href="/A319689/b319689.txt">Table of n, a(n) for n = 1..16384</a>
%H A319689 Antti Karttunen, <a href="/A319689/a319689.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A319689 (PARI)
%o A319689 up_to = 65537;
%o A319689 ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o A319689 A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
%o A319689 v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
%o A319689 A078898(n) = v078898[n];
%o A319689 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A319689 A319689(n) = if(1==n,0,my(m=Map(),s,k=0); while(1,if(!mapisdefined(m,s=A078898(n)), mapput(m,s,s); k++); if(!(n%2), return(k)); n = A064989(n)));
%Y A319689 Cf. A064989, A078898.
%Y A319689 Cf. also A246278, A319679.
%K A319689 nonn
%O A319689 1,21
%A A319689 _Antti Karttunen_, Nov 20 2018