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A095103
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4k+3 primes whose Legendre-vector is not valid Dyck-path.
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6
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19, 43, 67, 107, 127, 139, 163, 179, 211, 223, 227, 283, 307, 331, 347, 367, 379, 443, 463, 467, 487, 491, 499, 523, 547, 571, 587, 619, 631, 643, 683, 691, 727, 739, 787, 811, 823, 827, 859, 883, 907, 947, 967, 1019, 1051, 1087, 1123, 1163
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OFFSET
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1,1
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LINKS
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FORMULA
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MATHEMATICA
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L = {}; Do[p = Prime[k]; If[Mod[p, 4] == 3 && Min[Table[Sum[JacobiSymbol[n, p], {n, 0, m}], {m, 0, p - 1}]] < 0, L = Append[L, p]], {k, 1, 192}]; L (* From Jonathan Sondow, Oct 25 2011 *)
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PROG
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(PARI) isok(m) = {my(s=0); if(m%4==3&&isprime(m), for(i=1, m-1, if((s+=kronecker(i, m))<0, return(1)))); 0; } \\ Jinyuan Wang, Jul 20 2020
(Sage)
def is_Motzkin(n, k):
s = 0
for i in (1..k) :
s += jacobi_symbol(i, n)
if s < 0 : return false
return true
P = filter(is_prime, range(n+1)[3::4])
return filter(lambda m: not is_Motzkin(m, m//2), P)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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