A388301 a(n) is the number of steps to reach n again when the Sisyphus sequence (A350877) begins with n, or -1 if n is never reached.

7, 7, 7, 7, 3, 7, 25, 7, 1937682, 3, 23, 20, 16, 25, 18, 19, 161, 1937682, 149, 13, 30, 23, 26, 20, 50, 16, 30, 25, 43, 18, 26, 741, 55, 161, 839, 1937682, 68, 149, 39, 44, 1630, 30, 42, 481, 527813878, 26, 125, 49, 640, 50, 96, 32, 21120, 30, 129, 114, 107, 43, 124, 35

Offset

1,1

Comments

a(127) > 5261947751483 and a(211) > 1261930000000.

Links

Table of n, a(n) for n=1..60.

Karl-Heinz Hofmann, Table of n, a(n) for n=1..1014, with missing entries > 10^9 noted.

Example

a(10) = 3 because 3 steps are needed to end up again at 10:
Step 1: 10 is even and 10/2 = 5;
Step 2:  5 is  odd and 5 + 2 (= first prime)  =  7;
Step 3:  7 is  odd and 7 + 3 (= second prime) = 10.

Prog

(Python)
from itertools import count
from sympy import nextprime
A388301 = []
for n in range(1, 45):
    m, prime = n, 0
    for steps in count(1):
        if m % 2: m += (prime:=nextprime(prime))
        else: m //= 2
        if m == n: break
    A388301.append(steps)
print(A388301)

Crossrefs

Cf. A350877, A388038.

Sequence in context: A103983 A232127 A388255 * A195413 A083947 A269349

Adjacent sequences: A388298 A388299 A388300 * A388302 A388303 A388304

Keyword

nonn

Author

Karl-Heinz Hofmann, Sep 16 2025

Status

approved