A353054 Numbers k such that placing the last digit first gives 2k+1.

1052, 26315, 15789473, 3157894736, 421052631578, 2105263157894, 36842105263157, 1052631578947368421052, 26315789473684210526315, 15789473684210526315789473, 3157894736842105263157894736, 421052631578947368421052631578, 2105263157894736842105263157894, 36842105263157894736842105263157

Offset: 1

Author

Tanya Khovanova, Apr 20 2022

Keywords

• nonn
• base

Comments

The digits of all terms appear to be a substring of the digits 105263157894736842 (= A092697(2)) repeated. - Chai Wah Wu, Apr 23 2022

Examples

			2*1052 + 1 = 2105. Thus, 1052 is in this sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..389

Crossrefs

Other "rotate right" sequences: A035126, A035130.

Subsequence of A034180.

Programs

Mathematica

Select[Range[100000000], FromDigits[Prepend[Drop[IntegerDigits[#], -1], Last[IntegerDigits[#]]]] == 2 # + 1 &]

PARI

f(n) = if (n < 10, n, my(d=digits(n)); fromdigits(concat(d[#d], Vec(d, #d-1))));
isok(m) = f(m) == 2*m+1; \\ Michel Marcus, Apr 21 2022

Python

from itertools import count, islice
def A353054_gen(): # generator of terms
    for l in count(1):
        a, b = 10**l-2, 10**(l-1)-2
        for m in range(1,10):
            q, r = divmod(m*a-1,19)
            if r == 0 and b <= q - 2 <= a:
                yield 10*q+m
A353054_list = list(islice(A353054_gen(),20)) # Chai Wah Wu, Apr 23 2022

Extensions

a(4)-a(7) from Amiram Eldar, Apr 22 2022

a(8)-a(14) from Chai Wah Wu, Apr 23 2022