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 A322273 Smallest multiplication factors f, prime or 1, for all b (mod 840), coprime to 840 (= 4*7#), so that b*f is a nonzero square mod 8, mod 3, mod 5, and mod 7. 7
 1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 43, 71, 73, 79, 83, 41, 73, 101, 103, 107, 109, 113, 1, 127, 59, 113, 19, 47, 29, 79, 13, 43, 47, 1, 173, 11, 61, 283, 71, 193, 53, 31, 41, 211, 29, 103, 83, 61, 113, 71, 241, 127, 59, 37, 17, 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(4). The sequence is periodic, repeating itself after phi(840) = 192 terms. Its largest term is 311, which is A322269(4). In order to satisfy the conditions, both f and b must be coprime to 840. Otherwise, the product would be zero mod a prime <= 7. The b(n) corresponding to each a(n) is A008364(n). The first 15 terms are trivial: f=b, and then the product b*f naturally is a square modulo everything. LINKS Hans Ruegg, Table of n, a(n) for n = 1..192 EXAMPLE The 16th number coprime to 840 is 67. a(16) is 43, because 43 is the smallest prime by which we can multiply 67, so that the product (67*43 = 2881) is a square mod 8, mod 2, mod 3, mod 5, and mod 7. 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 29 05:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)