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A328761 The least integer k >= 0 for which A328578(k) = A257993(A276086(A276086(k))) = n.

%I A328761 #16 Oct 27 2019 17:32:43
%S A328761 1,0,2,4,10,20,28,82,116,148,208,418,838,1048,1466,1858,2276,4612,
%T A328761 9028,11546,16162,18478,23098,27688,30028,90086,147838,180178,240232,
%U A328761 297988,330328,390358,450238,480478,1021016,2039728,3033028,3573566,4594558,5105098,6606598,7147136,8168152,8678668,9699688,29099062,48498238,58198138,77597516,96996896,106696588,126095968
%N A328761 The least integer k >= 0 for which A328578(k) = A257993(A276086(A276086(k))) = n.
%C A328761 The sequence seems to be monotonic from the second term onward. If this holds, then this sequence (after the initial 1) gives also the positions of records in A328578. See also the scatterplot of A328578.
%H A328761 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328761 (PARI)
%o A328761 A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
%o A328761 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328761 A328578(n) = A257993(A276086(A276086(n)));
%o A328761 A328761(n) = for(k=0,oo,if(A328578(k)==n,return(k)));
%o A328761 (PARI)
%o A328761 A328761list(up_to) = { my(v=vector(up_to), k); for(n=0,oo,k=A328578(n); if(k>#v, return(v)); if(!v[k],v[k] = n; print("Found ",k, " at n=",n)); if(k>=#v,return(v))); };
%o A328761 v328761 = A328761list(52);
%o A328761 A328761(n) = if(2==n,0,v328761[n]);
%Y A328761 Column 1 of A328631.
%Y A328761 Cf. A257993, A276086, A328578.
%K A328761 nonn
%O A328761 1,3
%A A328761 _Antti Karttunen_, Oct 27 2019