A095092 Number of 4k+3 primes whose Legendre-vector is a Dyck-path (A095102) in range ]2^n,2^(n+1)].

1, 1, 1, 2, 2, 4, 7, 10, 16, 30, 51, 88, 153, 277, 509, 905, 1660, 3079, 5535, 10234, 19053

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• more

Links

• A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence
• Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]

Crossrefs

Cf. A095090, A095102.

Programs

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; }
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

Formula

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