A321366 a(n) is the least integer k greater than 1 such that n divides binomial(k, 2) = A000217(k-1).
2, 4, 3, 8, 5, 4, 7, 16, 9, 5, 11, 9, 13, 8, 6, 32, 17, 9, 19, 16, 7, 12, 23, 16, 25, 13, 27, 8, 29, 16, 31, 64, 12, 17, 15, 9, 37, 20, 13, 16, 41, 21, 43, 33, 10, 24, 47, 33, 49, 25, 18, 40, 53, 28, 11, 49, 19, 29, 59, 16, 61, 32, 28, 128, 26
Offset: 1
Links
- Kevin Long, Table of n, a(n) for n = 1..10000
- Kevin Long, Python code for sequence
Programs
-
PARI
a(n) = {my(s=1, k=2); while(s%n, s+=k; k++); k} \\ Andrew Howroyd, Aug 27 2019 (Python 3.8+) from itertools import combinations from math import prod from sympy import factorint, divisors from sympy.ntheory.modular import crt def A321366(n): plist = [p**q for p, q in factorint(2*n).items()] if len(plist) == 1: return int((2 - plist[0] % 2)*n) return 1+int(min(min(crt([m,2*n//m],[0,-1])[0],crt([2*n//m,m],[0,-1])[0]) for m in (prod(d) for l in range(1,len(plist)//2+1) for d in combinations(plist,l)))) # Chai Wah Wu, Jun 03 2021