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A292243 a(1) = 1; for n > 1, a(n) = 3*a(A253889(n)) + (n mod 3). 7
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 (list; graph; refs; listen; history; text; internal format)
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
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. also A292384.
Sequence in context: A217415 A213571 A185880 * A105201 A184537 A187809
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Sep 15 2017
STATUS
approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)