A292594 -id:A292594 - cp's OEIS frontend

A292590 a(1) = 0; and for n > 1, a(n) = 2*a(A285712(n)) + [0 == (n mod 3)].

0, 0, 1, 2, 0, 5, 10, 2, 21, 42, 4, 85, 0, 0, 171, 342, 10, 5, 684, 20, 1369, 2738, 4, 5477, 0, 42, 10955, 8, 84, 21911, 43822, 8, 21, 87644, 170, 175289, 350578, 0, 11, 701156, 0, 1402313, 40, 342, 2804627, 16, 684, 85, 5609254, 20, 11218509, 22437018, 10, 44874037, 89748074, 1368, 179496149, 168, 40, 43, 0, 2738, 1, 358992298, 5476, 717984597, 80, 8

Offset: 1

Antti Karttunen, Sep 20 2017

nonn

Binary expansion of a(n) encodes the positions of multiples of three in the path taken from n to the root in the binary trees like A245612 and A244154.

Cf. A079978, A244153, A245611, A285712, A292591, A292592, A292594.

Cf. also A292244, A292383.

f[n_] := f[n] = Which[n == 1, 0, Mod[n, 3] == 2, Ceiling[n/3], True, (Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1] + 1)/2]; a[n_] := a[n] = If[n == 1, n - 1, 2 a[f@ n] + Boole[Divisible[n, 3]]]; Array[a, 67] (* Michael De Vlieger, Sep 22 2017 *)

(define (A292590 n) (if (<= n 1) 0 (+ (if (zero? (modulo n 3)) 1 0) (* 2 (A292590 (A285712 n))))))

a(1) = 0; and for n > 1, a(n) = A079978(n) + 2*a(A285712(n)).
a(n) + A292591(n) = A245611(n).
a(A245612(n)) = A292592(n).
A000120(a(n)) = A292594(n).

A292595 a(n) = A000120(A292591(n)).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 3, 1, 3, 4, 2, 4, 2, 1, 4, 5, 2, 1, 6, 3, 6, 7, 1, 7, 3, 3, 7, 3, 4, 7, 8, 2, 2, 9, 4, 9, 10, 2, 1, 11, 1, 11, 4, 4, 11, 4, 5, 3, 12, 2, 12, 13, 1, 13, 14, 6, 14, 5, 3, 2, 4, 6, 1, 15, 7, 15, 5, 1, 15, 16, 7, 1, 5, 3, 16, 17, 3, 4, 18, 7, 3, 19, 3, 19, 5, 4, 19, 2, 7, 19, 20, 8, 5, 5, 2, 20, 21, 2, 21, 22, 9, 5, 7, 4, 2

Offset: 1

Antti Karttunen, Sep 20 2017

nonn

If n > 1, then locate the node which contains n in binary tree A245612 (or in its mirror-image A244154) and traverse from that node towards the root [by iterating the map n -> A285712(n)], at the same time counting all numbers of the form 3k+1 that occur on the path, down to the final 1. This count includes also n itself if it is of the form 3k+1, with k > 0 (thus a(1) = 0).

Antti Karttunen, Table of n, a(n) for n = 1..8505
Index entries for sequences computed from indices in prime factorization

Cf. A000120, A285712, A285715, A292591, A292594.

(define (A292595 n) (if (<= n 2) (- n 1) (+ (if (= 1 (modulo n 3)) 1 0) (A292595 (A285712 n)))))

a(1) = 0, a(2) = 1, and for n > 1, a(n) = a(A285712(n)) + [1 == (n mod 3)].
a(n) = A000120(A292591(n)).
a(n) + A292594(n) = A285715(n).

cp's OEIS Frontend

A292590 a(1) = 0; and for n > 1, a(n) = 2*a(A285712(n)) + [0 == (n mod 3)].

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