A034180 Numbers m with property that rotating digits of m right gives k*m + 1 for some k >= 1.

103, 1052, 1139, 2758, 26315, 206896, 1012658, 15789473, 137931034, 183673469, 3157894736, 421052631578, 1020408163265, 2105263157894, 13559322033898, 36842105263157, 241379310344827, 1525423728813559, 11392405063291139

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• base

Examples

			Rotating 103 gives 310 and 310 = 3 * 103 + 1. - _Sean A. Irvine_, Aug 04 2020
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..958

Programs

Python

from itertools import count, islice
def A034180_gen(): # generator of terms
    for l in count(1):
        clist = []
        for k in range(1,10):
            a, b = 10**l-k, 10**(l-1)-k
            for m in range(1,10):
                q, r = divmod(m*a-1,10*k-1)
                if r == 0 and b <= q - k <= a:
                    clist.append(10*q+m)
        yield from sorted(clist)
A034180_list = list(islice(A034180_gen(),20)) # Chai Wah Wu, Apr 23 2022

Extensions

Terms sorted and title clarified by Sean A. Irvine, Aug 04 2020

a(19) corrected by Chai Wah Wu, Apr 23 2022