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A389360
Smallest m >= 2*n such that binomial(m,n) is a multiple of m-i for all 0<=i<n, but one.
1
4, 6, 9, 12, 75, 30, 70, 56, 2403, 280, 3465, 210, 793, 4732, 3213, 1456, 31110, 612, 67203, 145540, 464646, 2640, 476938, 21000, 86550, 234026, 1053702, 34776, 37584001, 8100, 2301456, 77780756, 61924632, 26515138, 105846930, 665280, 622999377, 233999782, 510752034, 1154440
OFFSET
2,1
COMMENTS
Other known values: a(43) = 24458112 and a(47) = 3076480.
LINKS
Thomas Bloom, Problem 1063, Erdős Problems.
PROG
(SageMath)
def a(n):
m=2*n;
while 0<1:
t=binomial(m, n); S=[i for i in range(0, n) if t%(m-i)!=0];
if len(S)==1: return m;
else: m+=1
(PARI) isok(m, n) = my(b=binomial(m, n), nb=0); for (i=0, n-1, if (!(b % (m-i)), nb++)); nb==n-1;
a(n) = my(m=2*n); while (!isok(m, n), m++); m; \\ Michel Marcus, Oct 09 2025
(Python)
from itertools import count
from math import comb
def A389360(n):
c = comb(n<<1, n)
for m in count(n<<1):
s = 0
for i in range(n):
if c%(m-i):
s += 1
if s>1:
break
if s==1:
return m
c = c*(m+1)//(m+1-n) # Chai Wah Wu, Oct 14 2025
CROSSREFS
Cf. A007318.
Sequence in context: A078782 A165897 A020165 * A368196 A110607 A085802
KEYWORD
nonn
AUTHOR
Stijn Cambie, Oct 01 2025
EXTENSIONS
a(38)-a(40) from Chai Wah Wu, Oct 14 2025
a(41) from Stijn Cambie, Oct 01 2025
STATUS
approved