A361248 a(n) is the smallest integer k > 3 that satisfies k mod j <= 3 for all integers j in 1..n.

4, 4, 4, 4, 5, 6, 7, 8, 56, 72, 91, 651, 651, 1080, 1080, 1443, 20163, 20163, 246962, 246962, 246962, 609843, 2162162, 2162162, 29055601, 29055601, 107881202, 107881202, 205405203, 205405203, 3625549202, 5675443203, 8374212002, 8374212002, 8374212002, 8374212002, 131668891200, 131668891200

Offset: 1

Author

Andrew Cogliano, Mar 05 2023

Keywords

• nonn

Examples

			a(11)=91 since 91 mod 11 = 3, 91 mod 10 = 1, 91 mod 9 = 1, 91 mod 8 = 3, 91 mod 7 = 0, 91 mod 6 = 1, 91 mod 5 = 1, 91 mod 4 = 3, 91 mod 3 = 1, 91 mod 2 = 1, 91 mod 1 = 0 and 91 is the smallest integer greater than 3 where all of these remainders are 3 or less.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A003418 (all remainders 0).

Cf. A361246, A361247.

Programs

PARI

isok(k, n) = for (j=5, n, if ((k % j) > 3, return(0))); return(1);
a(n) = my(k=4); while(!isok(k, n), k++); k; \\ Michel Marcus, Mar 17 2023

Python

final=100
k=4
for n in range(1, final+1):
    j = n+1
    while (j > 3):
        j -= 1
        if k%j>3:
              k += j-(k%j)
              j = n+1
    print(k)

Formula

For n > 2, n <= a(n) < A003418(n). - Charles R Greathouse IV, Apr 27 2023