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A329898 a(n) is the position of 2*A025487(n) in A025487. 10

%I

%S 2,3,5,6,7,8,10,12,13,14,15,16,17,18,19,21,24,25,26,27,28,29,30,31,32,

%T 33,34,35,36,37,39,40,42,45,46,47,48,49,50,51,52,53,55,56,57,58,59,60,

%U 61,62,63,64,65,66,67,68,70,71,74,75,76,78,80,81,82,83,84,85,86,87,88,89,90,91,92,94,95,96,97,98,99,100

%N a(n) is the position of 2*A025487(n) in A025487.

%C Numbers k for which A007814(A025487(k)) > A007949(A025487(k)), i.e., numbers k for which the 2-adic valuation of A025487(k) is larger than its 3-adic valuation.

%C Numbers k for which A181815(k) is even.

%H Antti Karttunen, <a href="/A329898/b329898.txt">Table of n, a(n) for n = 1..10000</a>

%F For all n >= 1, A329904(a(n)) = n.

%t (* First, load the function f at A025487, then: *)

%t With[{s = Union@ Flatten@ f@ 6}, Map[If[2 # > Max@ s, Nothing, FirstPosition[s, 2 #][[1]] ] &, s]] (* _Michael De Vlieger_, Jan 11 2020 *)

%o (PARI)

%o upto_e = 64; \\ 64 -> 43608 terms.

%o A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980

%o A329898list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t, v025487); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t =

%o A283980(lista[i]); if(t <= u, listput(lista,t))); i++); v025487 = vecsort(Vec(lista)); lista = List([]); for(i=1,oo,if(!(t=vecsearch(v025487,2*(v025487[i]))),return(Vec(lista)), listput(lista,t))); };

%o v329898 = A329898list(upto_e);

%o A329898(n) = v329898[n];

%Y Cf. A329897 (complement), A330683 (and its permutation).

%Y Cf. A007814, A007949, A025487, A329904 (a left inverse), A329906.

%Y Positions of even terms in A181815, zeros in A330682.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 24 2019

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Last modified March 2 12:06 EST 2021. Contains 341750 sequences. (Running on oeis4.)