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URL: https://oeis.org/A377476

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A377476
Primes p such that 1..12 are quadratic residues modulo p.
1
479, 1151, 1319, 1559, 2351, 2689, 2999, 3529, 3671, 3911, 4751, 4919, 5519, 5569, 5711, 6551, 6599, 7559, 7561, 7681, 8089, 8761, 8951, 9239, 9241, 9601, 9719, 9769, 10391, 10559, 10799, 12049, 12239, 12721, 12911, 13151, 13729, 14159, 14281, 14759, 14951, 15671, 15791, 16631, 16921
OFFSET
1,1
COMMENTS
An odd prime p is a term if and only if the Legendre symbol Legendre(q|p) = 1 for all q = 2,3,5,7,11; i.e., each prime q <= 12 is a quadratic residue.
Prime p is a term if and only if all the following conditions are satisfied:
p == +-1 (mod 24)
p == +-1 (mod 10)
p == +-1, +-3, +-9 (mod 28)
p == +-1, +-5, +-7, +-9, +-19 (mod 44)
Prime p is a term if and only if it is congruent to any number in the attached file modulo 9240.
EXAMPLE
479 is a term of this sequence, since Legendre(b|479) = 1 for b = 1, 2, ..., 12.
MATHEMATICA
Select[Prime /@ Range[2000], And @@ Table[KroneckerSymbol[b, #] == 1, {b, Range[12]}] &]
PROG
(PARI) isok(p)={for(i=1, 12, if(kronecker(i, p)<0, return(0))); isprime(p)} \\ Andrew Howroyd, Feb 17 2025
CROSSREFS
Sequence in context: A056987 A323051 A025025 * A108256 A393084 A262222
KEYWORD
nonn
AUTHOR
Steven Lu, Feb 16 2025
STATUS
approved