This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
2357111317 is divisible by 11, and concatenation through 499 is required for divisibility by 11^2.
The concatenations short of the one ending with 61 are not divisible by 13, while that one is.
235711131719232931 is divisible by 17.
While the very first concatenation is divisible by 23, 23^2 does not divide any such number until 5861 is adjoined.
from sympy import nextprime def A185704(n): p, k, m = 2, 73**n, 10 q, m2 = p % k, m % k while True: p = nextprime(p) while p >= m: m *= 10 m2 = m % k q = (q*m2 + p) % k if q == 0: return p # Chai Wah Wu, May 01 2020
from sympy import nextprime def A185695(n): p, k, m = 2, 61**n, 10 q, m2 = p % k, m % k while True: p = nextprime(p) while p >= m: m *= 10 m2 = m % k q = (q*m2 + p) % k if q == 0: return p # Chai Wah Wu, May 01 2020
23571113171923293137 is divisible by 67^2.
from sympy import nextprime def A185698(n): p, k, m = 2, 67**n, 10 q, m2 = p % k, m % k while True: p = nextprime(p) while p >= m: m *= 10 m2 = m % k q = (q*m2 + p) % k if q == 0: return p # Chai Wah Wu, May 01 2020
The first concatenation of primes--23, 235, 2357, 235711, etc.--that is divisible by 19 concatenates through 271, and to get divisibility by 19^2 it's necessary to go through 1831.
Comments