The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A306501 Primes p such that 2, 3, 5, 7, ..., 37 are all quadratic nonresidues modulo p. 1
 163, 74093, 92333, 170957, 222643, 225077, 253507, 268637, 292157, 328037, 360293, 517613, 524453, 530837, 613637, 641093, 679733, 781997, 847997, 852893, 979373, 991027, 1096493, 1110413, 1333963, 1398053, 1730357, 1821893, 2004917, 2055307, 2056147, 2079173 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The prime number 163 is famous for having 2, 3, 5, 7, ..., 37 as quadratic nonresidues, because the smallest prime having 2, 3, 5, 7, ..., 41 as quadratic nonresidues, namely 74093, is 453.5 times larger. This is related to the fact that the quadratic field Q[sqrt(-163)] is a unique factorization domain. If p is in the sequence then so are all primes q with q == p (mod 29682952539240), where 29682952539240 = 2^3*3*5*7*11*13*17*19*23*29*31*37. In particular, the sequence is infinite. - Robert Israel, Mar 31 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..2694 MAPLE N:= 3*10^6: # to get all terms <= N S:= {seq(8*i+3, i=1..(N-3)/8)} union {seq(8*i+5, i=1..(N-5)/8)}: for p in select(isprime, [\$3..37]) do R:= select(t -> numtheory:-legendre(t, p) = 1, {\$1..p-1}); if p mod 4 = 1 then S:= remove(t -> member(t mod p, R), S) else S:= select(t -> member(t mod p, R) = evalb(t mod 4 = 3), S) fi; od: sort(convert(select(isprime, S), list)); # Robert Israel, Mar 31 2019 PROG (PARI) forprime(p=2, 1e6, if(sum(k=1, 37, isprime(k)*kronecker(k, p))==-12, print1(p, ", "))) CROSSREFS Cf. A191089. Sequence in context: A217963 A138200 A146504 * A247269 A145741 A247273 Adjacent sequences: A306498 A306499 A306500 * A306502 A306503 A306504 KEYWORD nonn AUTHOR Jianing Song, Feb 19 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 05:53 EST 2023. Contains 367630 sequences. (Running on oeis4.)