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A317753 Number of steps to reach 1 in 7x+-1 problem, or -1 if 1 is never reached. 1
0, 1, 13, 2, 10, 14, 18, 3, 7, 11, 53, 15, 19, 19, 23, 4, 27, 8, 50, 12, 73, 54, 16, 16, 58, 20, 20, 20, 43, 24, 24, 5, 47, 28, 325, 9, 70, 51, 32, 13, 13, 74, 272, 55, 55, 17, 17, 17, 276, 59, 40, 21, 40, 21, 21, 21, 63, 44, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The 7x+-1 problem is as follows. Start with any natural number n. If 4 divides n-1, multiply it by 7 and add 1; if 4 divides n+1, multiply it by 7 and subtract 1; otherwise divide it by 2. The 7x+-1 problem concerns the question whether we always reach 1.

The number of steps to reach 1 is also called the total stopping time.

Also the least positive k for which the iterate A317640^k(n) = 1.

LINKS

David Barina, Table of n, a(n) for n = 1..10000

D. Barina, 7x+-1: Close Relative of Collatz Problem, arXiv:1807.00908 [math.NT], 2018.

K. Matthews, David Barina's 7x+1 conjecture.

EXAMPLE

a(5)=10 because the trajectory of 5 is (5, 36, 18, 9, 64, 32, 16, 8, 4, 2, 1).

MATHEMATICA

f[n_] := Switch[Mod[n, 4], 0, n/2, 1, 7 n + 1, 2, n/2, 3, 7 n - 1]; a[n_] := Length@NestWhileList[f, n, # > 1 &] - 1; Array[a, 70] (* Robert G. Wilson v, Aug 07 2018 *)

PROG

(C)

int a(int n) {

        int s = 0;

        while( n != 1 ) {

                switch(n%4) {

                        case 1: n = 7*n+1; break;

                        case 3: n = 7*n-1; break;

                        default: n = n/2;

                }

                s++;

        }

        return s;

}

(PARI) a(n) = my(nb=0); while(n != 1, if (!((n-1)%4), n = 7*n+1, if (!((n+1)%4), n = 7*n-1, n = n/2)); nb++); nb; \\ Michel Marcus, Aug 06 2018

CROSSREFS

Cf. A317640 (7x+-1 function), A006577 (3x+1 equivalent).

Sequence in context: A100081 A078197 A070704 * A298059 A298708 A124686

Adjacent sequences:  A317750 A317751 A317752 * A317754 A317755 A317756

KEYWORD

nonn,easy,hear,look

AUTHOR

David Barina, Aug 06 2018

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)