A357913 Another test for divisibility by the n-th prime (see Comments for precise definition).

5, 10, 4, 12, 2, 7, 3, 28, 26, 37, 13, 33, 16, 6, 55, 47, 64, 22, 8, 25, 9, 68, 91, 31, 75, 11, 34, 89, 118, 96, 14, 15, 136, 110, 49, 117, 52, 18, 163, 172, 58, 138, 20, 190, 67, 159, 23, 70, 24, 217, 226, 180, 79, 27, 244, 194, 253, 85, 88, 215, 280, 94, 222, 298, 236, 243

Offset

4,1

Comments

Given a number M, delete its last digit d, then add d*a(n). If the result is divisible by prime(n), then M is also divisible by prime(n). This process may be repeated.

a(n) can be quickly calculated by finding the smallest multiple of prime(n) ending in 9, adding one, and dividing that result by 10. E.g., 7 -> 49 -> 5, 11 -> 99 -> 10, 13 -> 39 -> 4, 17 -> 119 -> 12, 19 -> 19 -> 2.

Links

Table of n, a(n) for n=4..69.

Formula

a(n) = prime(n) - A103876(n).

a(n) = (A114013(n) + 1)/10. - Hugo Pfoertner, Jan 28 2023

Prog

(Python)
import sympy
[pow(10, -1, p) for p in sympy.primerange(7, 348)]

Crossrefs

Cf. A103876, A078606, A114013.

Sequence in context: A054513 A295121 A066200 * A053822 A262922 A276652

Adjacent sequences: A357910 A357911 A357912 * A357914 A357915 A357916

Keyword

nonn,base

Author

Nicholas Stefan Georgescu, Jan 18 2023

Status

approved