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Number of 4k+3 primes whose Legendre-vector is a Dyck-path (A095102) in range ]2^n,2^(n+1)].
4

%I #10 Jul 20 2020 06:41:16

%S 1,1,1,2,2,4,7,10,16,30,51,88,153,277,509,905,1660,3079,5535,10234,

%T 19053

%N Number of 4k+3 primes whose Legendre-vector is a Dyck-path (A095102) in range ]2^n,2^(n+1)].

%H A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%H <a href="/index/Pri#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>

%F a(n) = A095008(n) - A095093(n).

%o (PARI) is(m) = {if(!isprime(m), return(0)); my(s=0); for(i=1, m-1, if((s+=kronecker(i, m))<0, return(0))); 1; }

%o a(n) = {my(c=0); forstep(m=2^n+3*(n>1), 2^(n+1), 4, c+=is(m)); c; } \\ _Jinyuan Wang_, Jul 20 2020

%Y Cf. A095090, A095102.

%K nonn,more

%O 1,4

%A _Antti Karttunen_, Jun 01 2004