A095102 Odd primes p for which all sums Sum_{i=1..u} L(i/p) (with u ranging from 1 to (p-1)) are nonnegative, where L(i/p) is Legendre symbol of i and p, defined to be 1 if i is a quadratic residue (mod p) and -1 if i is a quadratic non-residue (mod p).
3, 7, 11, 23, 31, 47, 59, 71, 79, 83, 103, 131, 151, 167, 191, 199, 239, 251, 263, 271, 311, 359, 383, 419, 431, 439, 479, 503, 563, 599, 607, 647, 659, 719, 743, 751, 839, 863, 887, 911, 919, 971, 983, 991, 1031, 1039, 1063, 1091, 1103, 1151
Offset: 1
Keywords
Links
- T. D. Noe, Table of n, a(n) for n=1..1000
- Peter Borwein, Stephen K.K. Choi and Michael Coons, Completely multiplicative functions taking values in {-1,1}, arXiv:0809.1691 [math.NT], 2008.
- A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence
Crossrefs
Programs
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Mathematica
isMotzkin[n_, k_] := Module[{s = 0, r = True}, Do[s += JacobiSymbol[i, n]; If[s < 0, r = False; Break[]], {i, 1, k}]; r]; A095102[max_] := Select[ Range[3, max, 4], PrimeQ[#] && isMotzkin[#, Quotient[#, 2]]&]; A095102[1151] (* Jean-François Alcover, Feb 16 2018, after Peter Luschny *) -
PARI
isok(m) = {if(!isprime(m-(m<3)), return(0)); my(s=0); for(i=1, m-1, if((s+=kronecker(i, m))<0, return(0))); 1; } \\ Jinyuan Wang, Jul 20 2020 -
Sage
def A095102_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(3, n+1, 4)) return filter(lambda m: is_Motzkin(m, m//2), P) A095102_list(1151) # Peter Luschny, Aug 09 2012
Formula
a(n) = 4*A095272(n) + 3.
Comments