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A318489 Number of steps to reach a lower number than starting value in 7x+-1 problem, or 0 if never reached. 1
0, 1, 12, 1, 8, 1, 4, 1, 4, 1, 42, 1, 8, 1, 4, 1, 4, 1, 23, 1, 20, 1, 4, 1, 4, 1, 12, 1, 16, 1, 4, 1, 4, 1, 282, 1, 12, 1, 4, 1, 4, 1, 229, 1, 50, 1, 4, 1, 4, 1, 8, 1, 35, 1, 4, 1, 4, 1, 8, 1, 50, 1, 4, 1, 4, 1, 46, 1, 8, 1, 4, 1, 4, 1, 225, 1, 8, 1, 4, 1, 4, 1, 35, 1, 16, 1, 4, 1, 4, 1, 46, 1, 27, 1, 4, 1, 4, 1, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The least positive k for which the iterate A317640^k(n) < n.

Also called the dropping time, glide, or stopping time.

a(2n) = 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) = 8 because the trajectory is (5, 36, 18, 9, 64, 32, 16, 8, 4, 2, 1, ...) and the first lower number is 4. Thus 8 steps to reach the value 4 starting from the value 5.

PROG

(C)

int a(int n0) {

        if( n0 == 1 ) return 0;

        int s = 0;

        for(int n = n0; n >= n0; s++) {

                switch(n%4) {

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

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

                        default: n = n/2;

                }

        }

        return s;

}

(PARI) a7(n) = {my(m=(n+2)%4-2); if(m%2, 7*n + m, n/2)};

a(n) = if (n==1, 0, my(nb=1, m=n, nm); while((nm=a7(m)) >= n, m = nm; nb++); nb); \\ Michel Marcus, Aug 28 2018

CROSSREFS

Cf. A317640 (7x+-1 function), A102419 (3x+1 equivalent).

Sequence in context: A140378 A085094 A010214 * A121985 A245839 A068329

Adjacent sequences:  A318486 A318487 A318488 * A318490 A318491 A318492

KEYWORD

nonn,easy

AUTHOR

David Barina, Aug 27 2018

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)