A095273 -id:A095273 - cp's OEIS frontend

A095278 Numbers k such that 4k + 3 is prime.

0, 1, 2, 4, 5, 7, 10, 11, 14, 16, 17, 19, 20, 25, 26, 31, 32, 34, 37, 40, 41, 44, 47, 49, 52, 55, 56, 59, 62, 65, 67, 70, 76, 77, 82, 86, 89, 91, 94, 95, 104, 107, 109, 110, 115, 116, 119, 121, 122, 124, 125, 130, 136, 140, 142, 146, 149, 151, 154, 157, 160, 161, 164

Offset: 1

Antti Karttunen, Jun 01 2004

Iain Fox, Table of n, a(n) for n = 1..10000

Cf. A002145. Complement of A095277. Union of A095272 and A095273. Cf. also A005098.

Filtered([1..170],n->IsPrime(4*n+3)); # Muniru A Asiru, Oct 29 2018

[n: n in [0..1000]|IsPrime(4*n+3)] // Vincenzo Librandi, Nov 16 2010

A095278:=n->`if`(isprime(4*n+3), n, NULL): seq(A095278(n), n=0..300); # Wesley Ivan Hurt, Jun 29 2015

Select[Range[0,200], PrimeQ[4#+3]&] (* Harvey P. Dale, Aug 15 2013 *)

is(n)=isprime(4*n+3) \\ Charles R Greathouse IV, Jul 01 2013

a(n) = (A002145(n) - 3)/4.

A095103 4k+3 primes whose Legendre-vector is not valid Dyck-path.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 01 2004

nonn

A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Intersection of A000040 and A095101. Complement of A095102 in A002145.

Cf. A095093, A095108 (diving indices).

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 *)

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

def A095103_list(n) :
    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)
A095103_list(1163) # Peter Luschny, Aug 08 2012

a(n) = 4*A095273(n) + 3.

A095272 a(n) = (A095102(n)-3)/4.

Original entry on oeis.org

0, 1, 2, 5, 7, 11, 14, 17, 19, 20, 25, 32, 37, 41, 47, 49, 59, 62, 65, 67, 77, 89, 95, 104, 107, 109, 119, 125, 140, 149, 151, 161, 164, 179, 185, 187, 209, 215, 221, 227, 229, 242, 245, 247, 257, 259, 265, 272, 275, 287, 305, 307, 319, 329, 349

Offset: 1

Antti Karttunen, Jun 01 2004

nonn

A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Complement of A095273 in A095278, subset of A095274.

A095275 a(n) = (A095101(n)-3)/4.

Original entry on oeis.org

4, 10, 12, 16, 22, 24, 26, 28, 30, 31, 34, 36, 38, 40, 44, 46, 48, 50, 51, 52, 54, 55, 56, 58, 61, 64, 66, 68, 70, 72, 76, 78, 80, 82, 84, 86, 88, 91, 94, 96, 100, 102, 105, 106, 108, 110, 112, 114, 115, 116, 118, 120, 121, 122, 124, 126, 128, 130, 132

Offset: 0

Antti Karttunen, Jun 01 2004

nonn

Antti Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Cf. A095101. Complement of A095274. Subset: A095273.

cp's OEIS Frontend

A095278 Numbers k such that 4k + 3 is prime.

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A095103 4k+3 primes whose Legendre-vector is not valid Dyck-path.

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A095272 a(n) = (A095102(n)-3)/4.

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A095275 a(n) = (A095101(n)-3)/4.

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