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 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. 7
 1, 5, 7, 11, 13, 17, 19, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS Table of n, a(n) for n=1..8. EXAMPLE 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. PROG (PARI) QresCode(n, nPrimes) = { code = bitand(n, 7)>>1; for (j=2, nPrimes, x = Mod(n, prime(j)); if (issquare(x), code += (1<

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Last modified May 20 02:53 EDT 2024. Contains 372703 sequences. (Running on oeis4.)