A358240 Consider all invertible residues mod n. For each residue, find the smallest product of three primes (A014612) which is in that residue class mod n. a(n) is the greatest of these.

8, 27, 28, 45, 66, 175, 45, 105, 76, 171, 102, 325, 165, 261, 124, 273, 230, 385, 188, 369, 268, 255, 175, 475, 284, 549, 436, 477, 285, 1309, 332, 385, 430, 927, 318, 1127, 442, 639, 610, 657, 595, 1075, 742, 805, 724, 637, 646, 1705, 642, 741, 670, 1005, 885, 1435, 801, 1705, 1105, 873, 1004, 2821, 938, 873, 844

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Ramachandran Balasubramanian, Olivier Ramaré, and Priyamvad Srivastav, Product of three primes in large arithmetic progressions, arXiv:2208.04031 [math.NT], 2022.

Formula

A result of Balasubramanian, Ramaré, & Srivastav proves that a(n) < n^e for each e > 9/2 and large enough n depending on e.

Example

The least product of 3 primes = 1 mod 3 is 28, while the least = 2 mod 3 is 8, so a(2) = 28.

Prog

(PARI) firstTri(m)=my(mod=m.mod); forprime(p=2, , if(mod%p==0, next); forprime(q=2, p, if(mod%q==0, next); forprimestep(r=2, q, m/p/q, return(p*q*r))))
a(n)=my(r=8); for(k=1, n-1, if(gcd(k, n)>1, next); r=max(firstTri(Mod(k, n)), r)); r

Crossrefs

All terms are in A014612.

Cf. A038026, A085420.

Sequence in context: A335018 A070498 A364875 * A084698 A070497 A070496

Adjacent sequences: A358237 A358238 A358239 * A358241 A358242 A358243

Keyword

nonn

Author

Charles R Greathouse IV, Jan 18 2023

Extensions

Corrected by Charles R Greathouse IV, May 10 2023

Status

approved