A292243 - OEIS

%I #17 Sep 18 2017 09:22:56

%S 1,5,3,16,17,9,49,11,33,160,50,156,52,53,147,88,29,27,82,149,474,457,

%T 35,453,106,101,441,151,482,303,265,152,483,250,470,1449,1441,158,480,

%U 1429,161,1407,469,443,1371,298,266,318,1348,89,969,961,83,954,910,248,897,268,449,1455,322,1424,99,808,1373,738,1366,107

%N a(1) = 1; for n > 1, a(n) = 3*a(A253889(n)) + (n mod 3).

%C a(n) encodes in its base-3 representation the succession of modulo 3 residues obtained when map x -> A253889(x), starting from x=n, is iterated down to the eventual 1.

%H Antti Karttunen, <a href="/A292243/b292243.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(1) = 1; for n > 1, a(n) = 3*a(A253889(n)) + A010872(n).

%t f[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; g[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; a[1] = 1; a[n_] := a[n] = 3 a[Floor@ g[Floor[f[n]/2]]] + Mod[n, 3]; Array[a, 68] (* _Michael De Vlieger_, Sep 16 2017 *)

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_

%o A048673(n) = (A003961(n)+1)/2;

%o 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 A064216(n) = A064989((2*n)-1);

%o A253889(n) = if(1==n,n,A048673(A064216(n)\2));

%o A292243(n) = if(1==n,n,((n%3) + 3*A292243(A253889(n))));

%o (Scheme, with memoization-macro definec)

%o (definec (A292243 n) (if (= 1 n) n (+ (modulo n 3) (* 3 (A292243 (A253889 n))))))

%Y Cf. A010872, A048673, A064216, A253889, A292244, A292245, A292246.

%Y Cf. also A292384.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Sep 15 2017