A322271 Smallest multiplication factors f, prime or 1, for all b (mod 24), coprime to 24, so that b*f is a nonzero square mod 8 and mod 3.

1, 5, 7, 11, 13, 17, 19, 23

Offset: 1

Author

Hans Ruegg, Dec 01 2018

Keywords

• nonn
• fini
• full

Comments

See sequence A322269 for further explanations. This sequence is related to A322269(2).

The sequence is periodic, repeating itself after phi(24) terms. Its largest term is 23, which is A322269(2). In order to satisfy the conditions, both f and b must be coprime to 24.

The b(n) corresponding to each a(n) is A007310(n).

In this case, the sequence is trivial, since each term is being multiplied by itself. The next related sequence, A322272, corresponding to A322269(3), already has several nontrivial terms.

Examples

			The 4th number coprime to 24 is 11. a(4) is 11, because 11 is the smallest prime by which we can multiply 11, so that the product (11*11 = 121) is a square mod 8 and mod 3.
		

Crossrefs

Cf. A322269, A322272, A322273, A322274, A322275, A007310.

Programs

PARI

QresCode(n, nPrimes) = {
  code = bitand(n,7)>>1;
  for (j=2, nPrimes,
    x = Mod(n,prime(j));
    if (issquare(x), code += (1<A322271, sequence(3) returns A322272, ... sequence(6) returns A322275.