A292243 a(1) = 1; for n > 1, a(n) = 3*a(A253889(n)) + (n mod 3).

1, 5, 3, 16, 17, 9, 49, 11, 33, 160, 50, 156, 52, 53, 147, 88, 29, 27, 82, 149, 474, 457, 35, 453, 106, 101, 441, 151, 482, 303, 265, 152, 483, 250, 470, 1449, 1441, 158, 480, 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

Offset

1,2

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

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

Mathematica

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 *)

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A048673(n) = (A003961(n)+1)/2;
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)};
A064216(n) = A064989((2*n)-1);
A253889(n) = if(1==n, n, A048673(A064216(n)\2));
A292243(n) = if(1==n, n, ((n%3) + 3*A292243(A253889(n))));
(Scheme, with memoization-macro definec)
(definec (A292243 n) (if (= 1 n) n (+ (modulo n 3) (* 3 (A292243 (A253889 n))))))

Crossrefs

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

Cf. also A292384.

Sequence in context: A217415 A213571 A185880 * A105201 A184537 A187809

Adjacent sequences: A292240 A292241 A292242 * A292244 A292245 A292246

Keyword

nonn,base

Author

Antti Karttunen, Sep 15 2017

Status

approved